{"id":188,"date":"2022-04-13T10:16:49","date_gmt":"2022-04-13T10:16:49","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=188"},"modified":"2024-08-23T17:40:40","modified_gmt":"2024-08-23T17:40:40","slug":"j-2-complete-a-table-quadratic-equations","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/j-2-complete-a-table-quadratic-equations\/","title":{"rendered":"J.2 Complete a table: quadratic equations"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Complete a table: quadratic equations<\/strong><\/h2>\n\n\n\n<p class=\"has-large-font-size\"><strong>Key notes !<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-d2e3d4f8325ebd7f6c91da364c5b6cad\" style=\"color:#c8f31d\"><strong>1. Understanding Quadratic Equations<\/strong><\/h3>\n\n\n\n<p>A quadratic equation is a second-degree polynomial equation of the form:<\/p>\n\n\n\n<p><br>f(x) = ax^2 + bx + c<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( a ), ( b ), and ( c ) are constants.<\/li>\n\n\n\n<li>( a not eqauls to 0 ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-22cb3afe477fd0e0307e087ce356969e\" style=\"color:#fd1616\"><strong>2. Purpose of Creating a Table<\/strong><\/h3>\n\n\n\n<p>Creating a table helps to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Visualize the behavior of the quadratic function.<\/li>\n\n\n\n<li>Identify key points such as the vertex, axis of symmetry, roots (if any), and the y-intercept.<\/li>\n\n\n\n<li>Understand how the function changes as ( x ) varies.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-7ef559a12d46dc6c701dd9a57456bfed\" style=\"color:#f9ca22\"><strong>3. Steps to Create a Table for a Quadratic Equation<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-bf49235c316965b07f635ecabfa4babf\" style=\"color:#d2cc1c\"><strong>Step 1: Choose a Range of ( x ) Values<\/strong><\/h4>\n\n\n\n<p>Select a range of ( x ) values that are evenly spaced and cover both negative and positive values. This ensures that the table captures the behavior of the quadratic function around its vertex and across the x-axis.<\/p>\n\n\n\n<p>For example, if the quadratic equation is ( f(x) = 2x^2 &#8211; 3x + 1 ), you might choose ( x ) values such as (-2, -1, 0, 1, 2).<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-05c695293739a21cd73c37fa9aff7f7f\" style=\"color:#94b038\"><strong>Step 2: Substitute ( x ) Values into the Equation<\/strong><\/h4>\n\n\n\n<p>For each chosen ( x ) value, substitute it into the quadratic equation to find the corresponding ( f(x) ) value. This involves simple arithmetic to evaluate the expression.<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-40038095422b0d02a9ebf095eba79901\" style=\"color:#6c30b0\"><strong>Step 3: Calculate ( f(x) ) for Each ( x ) Value<\/strong><\/h4>\n\n\n\n<p>Perform the calculation for each ( x ) value and record the result.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-6512642f5829fba1b097f29f0536da46\" style=\"color:#c6d823\"><strong>4. Example of Completing a Table<\/strong><\/h3>\n\n\n\n<p>Let&#8217;s consider the quadratic equation:<\/p>\n\n\n\n<p><br>f(x) = x^2 &#8211; 4x + 3<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-6ae413aabbd24f5e9bab99b0906acc41\" style=\"color:#f2b706\"><strong>Step-by-Step Table Creation<\/strong><\/h4>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Select ( x ) values<\/strong>: Choose values around the expected vertex, such as ( -1, 0, 1, 2, 3, 4, 5 ).<\/li>\n\n\n\n<li><strong>Create the table<\/strong>:<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>( x )<\/th><th>Calculation<\/th><th>( f(x) )<\/th><\/tr><\/thead><tbody><tr><td>-1<\/td><td>((-1)^2 &#8211; 4(-1) + 3)<\/td><td>( 1 + 4 + 3 = 8 )<\/td><\/tr><tr><td>0<\/td><td>(0^2 &#8211; 4(0) + 3)<\/td><td>( 0 + 0 + 3 = 3 )<\/td><\/tr><tr><td>1<\/td><td>(1^2 &#8211; 4(1) + 3)<\/td><td>( 1 &#8211; 4 + 3 = 0 )<\/td><\/tr><tr><td>2<\/td><td>(2^2 &#8211; 4(2) + 3)<\/td><td>( 4 &#8211; 8 + 3 = -1 )<\/td><\/tr><tr><td>3<\/td><td>(3^2 &#8211; 4(3) + 3)<\/td><td>( 9 &#8211; 12 + 3 = 0 )<\/td><\/tr><tr><td>4<\/td><td>(4^2 &#8211; 4(4) + 3)<\/td><td>( 16 &#8211; 16 + 3 = 3 )<\/td><\/tr><tr><td>5<\/td><td>(5^2 &#8211; 4(5) + 3)<\/td><td>( 25 &#8211; 20 + 3 = 8 )<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Final Table:<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>( x )<\/th><th>( f(x) )<\/th><\/tr><\/thead><tbody><tr><td>-1<\/td><td>8<\/td><\/tr><tr><td>0<\/td><td>3<\/td><\/tr><tr><td>1<\/td><td>0<\/td><\/tr><tr><td>2<\/td><td>-1<\/td><\/tr><tr><td>3<\/td><td>0<\/td><\/tr><tr><td>4<\/td><td>3<\/td><\/tr><tr><td>5<\/td><td>8<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-836a81ea4a858ac50dfd08d6b59f3895\" style=\"color:#e68b1b\"><strong>5. Interpreting the Table<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Vertex<\/strong>: The lowest (or highest for negative (a)) point on the table is the vertex. In this case, at ( x = 2 ), ( f(x) = -1 ) suggests the vertex is at (2, -1).<\/li>\n\n\n\n<li><strong>Axis of Symmetry<\/strong>: The x-value of the vertex (x = 2) acts as the line of symmetry for the parabola.<\/li>\n\n\n\n<li><strong>Roots<\/strong>: The x-values where ( f(x) = 0 ) are the roots of the equation. In this case, ( x = 1 ) and ( x = 3 ).<\/li>\n\n\n\n<li><strong>Y-Intercept<\/strong>: The value of ( f(x) ) when ( x = 0 ) is the y-intercept. Here, it\u2019s 3.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-4ed0e18322081209856b181489aedffd\" style=\"color:#bcf401\"><strong>6. Graphing Using the Table<\/strong><\/h3>\n\n\n\n<p>Plotting these ( (x, f(x)) ) points on a coordinate plane helps visualize the parabolic shape of the quadratic equation. You can use the table data to sketch the curve, marking key points like the vertex, intercepts, and roots.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#edbcbc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-151a0d24e320a43314fc62d4a1593128\" style=\"color:#b00012\"><strong>Complete the table.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\"><em>f<\/em>(<em>p<\/em>) =&nbsp;<em>p<\/em><sup>2<\/sup>&nbsp;\u2212 4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><em>p<\/em><\/td><td class=\"has-text-align-center\" data-align=\"center\"><em>f<\/em>(<em>p<\/em>)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<p>The first&nbsp;<em>p<\/em>-value&nbsp;in the table is&nbsp;-2. Evaluate&nbsp;<em>f<\/em>(<em>p<\/em>) =&nbsp;<em>p<\/em><sup>2<\/sup>&nbsp;\u2212 4&nbsp;for&nbsp;<em>p<\/em>&nbsp;=&nbsp;-2.<\/p>\n\n\n\n<p>f (p) = p<sup>2 <\/sup> &#8211; 4.<\/p>\n\n\n\n<p>        = (-2)<sup>2<\/sup>  &#8211; 4    plug in p = -2<\/p>\n\n\n\n<p>        = 4 &#8211; 4    Square<\/p>\n\n\n\n<p>        = 0    Subtract<\/p>\n\n\n\n<p>When&nbsp;<em>p<\/em>&nbsp;=&nbsp;-2,&nbsp;<em>f<\/em>(<em>p<\/em>) = 0. Complete the first row of the table.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\"><em>f<\/em>(<em>p<\/em>) =&nbsp;<em>p<\/em><sup>2<\/sup>&nbsp;\u2212 4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><em>p<\/em><\/td><td class=\"has-text-align-center\" data-align=\"center\"><em>f<\/em>(<em>p<\/em>)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Next, evaluate&nbsp;<em>f<\/em>(<em>p<\/em>) =&nbsp;<em>p<\/em><sup>2<\/sup>&nbsp;\u2212 4&nbsp;for&nbsp;<em>p<\/em>&nbsp;=&nbsp;-1.<\/p>\n\n\n\n<p>f (p) = p<sup>2 <\/sup> &#8211; 4.<\/p>\n\n\n\n<p>        = (-1)<sup>2<\/sup>  &#8211; 4    plug in p = -1<\/p>\n\n\n\n<p>        = 1 &#8211; 4    Square<\/p>\n\n\n\n<p>         = -3   Subtract<\/p>\n\n\n\n<p>When&nbsp;<em>p<\/em>&nbsp;=&nbsp;-1,&nbsp;<em>f<\/em>(<em>p<\/em>) =&nbsp;-3. Complete the second row of the table.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\"><em>f<\/em>(<em>p<\/em>) =&nbsp;<em>p<\/em><sup>2<\/sup>&nbsp;\u2212 4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><em>p<\/em><\/td><td class=\"has-text-align-center\" data-align=\"center\"><em>f<\/em>(<em>p<\/em>)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">-3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Complete the rest of the table the same way.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\"><em>f<\/em>(<em>p<\/em>) =&nbsp;<em>p<\/em><sup>2<\/sup>&nbsp;\u2212 4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><em>p<\/em><\/td><td class=\"has-text-align-center\" data-align=\"center\"><em>f<\/em>(<em>p<\/em>)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">-3<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">-4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">-3<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c0c0e0\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-151a0d24e320a43314fc62d4a1593128\" style=\"color:#b00012\"><strong>Complete the table.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\"><em>f<\/em>(<em>r<\/em>) =&nbsp;<em>r<\/em><sup>2<\/sup>&nbsp;+ 10<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><em>r<\/em><\/td><td class=\"has-text-align-center\" data-align=\"center\"><em>f<\/em>(<em>r<\/em>)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<p>The first&nbsp;R-value&nbsp;in the table is&nbsp;-1. Evaluate&nbsp;<em>f<\/em>(<em>r<\/em>) =&nbsp;<em>r<\/em><sup>2<\/sup>&nbsp;+ 10&nbsp;for&nbsp;<em>r<\/em>&nbsp;=&nbsp;-1.<\/p>\n\n\n\n<p>f (r)  = r<sup>2<\/sup> +10<\/p>\n\n\n\n<p>        = (-1)<sup>2<\/sup> + 10       plug in r = -1<\/p>\n\n\n\n<p>        = 1 + 10            Square<\/p>\n\n\n\n<p>         = 11                   Add<\/p>\n\n\n\n<p>When&nbsp;<em>r<\/em>&nbsp;=&nbsp;-1,&nbsp;<em>f<\/em>(<em>r<\/em>) = 11. Complete the first row of the table.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\">f(<em>r<\/em>) =&nbsp;<em>r<\/em><sup>2<\/sup>&nbsp;+ 10<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><em>r<\/em><\/td><td class=\"has-text-align-center\" data-align=\"center\"><em>f<\/em>(<em>r<\/em>)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">11<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Next, evaluate&nbsp;<em>f<\/em>(<em>r<\/em>) =&nbsp;<em>r<\/em><sup>2<\/sup>&nbsp;+ 10&nbsp;for&nbsp;<em>r<\/em>&nbsp;= 0.<\/p>\n\n\n\n<p>f (r)  = r<sup>2<\/sup> +10<\/p>\n\n\n\n<p>        = (0)<sup>2<\/sup> + 10 plug in r = 0<\/p>\n\n\n\n<p>        = 0 + 10  Square<\/p>\n\n\n\n<p>         = 10  Add<\/p>\n\n\n\n<p>When&nbsp;<em>r<\/em>&nbsp;= 0,&nbsp;<em>f<\/em>(<em>r<\/em>) = 10. Complete the second row of the table.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\">f(<em>r<\/em>) =&nbsp;<em>r<\/em><sup>2<\/sup>&nbsp;+ 10<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><em>r<\/em><\/td><td class=\"has-text-align-center\" data-align=\"center\"><em>f<\/em>(<em>r<\/em>)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">11<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Complete the rest of the table the same way.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\">f(<em>r<\/em>) =&nbsp;<em>r<\/em><sup>2<\/sup>&nbsp;+ 10<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><em>r<\/em><\/td><td class=\"has-text-align-center\" data-align=\"center\">f(r)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">11<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">11<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">2<\/td><td class=\"has-text-align-center\" data-align=\"center\">14<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#a4e1ac\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-2f26ac54ee3943703787358c6e518d60\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-151a0d24e320a43314fc62d4a1593128\" style=\"color:#b00012\"><strong>Complete the table.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\">f(j) =&nbsp;j<sup>2<\/sup><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">j<\/td><td class=\"has-text-align-center\" data-align=\"center\">f(j)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\"><\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<p>The first&nbsp;<em>j<\/em>-value&nbsp;in the table is&nbsp;-2. Evaluate&nbsp;<em>f<\/em>(<em>j<\/em>) =&nbsp;<em>j<\/em><sup>2<\/sup>&nbsp;for&nbsp;<em>j<\/em>&nbsp;=&nbsp;-2.<\/p>\n\n\n\n<p>f (j)  = j<sup>2<\/sup> <\/p>\n\n\n\n<p>        = (-2 )<sup>2<\/sup>  plug in j = &#8211; 2<\/p>\n\n\n\n<p>        = 4  Square<\/p>\n\n\n\n<p>  When&nbsp;<em>j<\/em>&nbsp;=&nbsp;-2,&nbsp;<em>f<\/em>(<em>j<\/em>) = 4. Complete the first row of the table.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\">f(j) =&nbsp;j<sup>2<\/sup><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">j<\/td><td class=\"has-text-align-center\" data-align=\"center\"><em>f(j)<\/em><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Next, evaluate&nbsp;<em>f<\/em>(<em>j<\/em>) =&nbsp;<em>j<\/em><sup>2<\/sup>&nbsp;for&nbsp;<em>j<\/em>&nbsp;=&nbsp;-1.<\/p>\n\n\n\n<p>f (j)  = j<sup>2<\/sup> <\/p>\n\n\n\n<p>        = (-1 )<sup>2<\/sup>            plug in j = &#8211; 1<\/p>\n\n\n\n<p>        = 1                  Square<\/p>\n\n\n\n<p>When&nbsp;<em>j<\/em>&nbsp;=&nbsp;-1,&nbsp;<em>f<\/em>(<em>j<\/em>) = 1. Complete the second row of the table.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\">f(j) =&nbsp;j<sup>2<\/sup><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">j<\/td><td class=\"has-text-align-center\" data-align=\"center\">f(j)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">?<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Complete the rest of the table the same way.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\" colspan=\"2\">f(j) =&nbsp;j<sup>2<\/sup><\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\"><em>j<\/em><\/td><td class=\"has-text-align-center\" data-align=\"center\">f(j)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-2<\/td><td class=\"has-text-align-center\" data-align=\"center\">4<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">-1<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><td class=\"has-text-align-center\" data-align=\"center\">0<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">let&#8217;s practice!<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76676\/788\/161\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-49.png\" alt=\"\" class=\"wp-image-6932\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-49.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-49-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-49-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/76714\/094\/818\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-67.png\" alt=\"\" class=\"wp-image-6934\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-67.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-67-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-67-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Complete a table: quadratic equations Key notes ! 1. Understanding Quadratic Equations A quadratic equation is a second-degree polynomial equation of the form: f(x) = ax^2 + bx + c Where: 2. Purpose of Creating a Table Creating a table helps to: 3. Steps to Create a Table for a Quadratic Equation Step 1: Choose<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/j-2-complete-a-table-quadratic-equations\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.2 Complete a table: quadratic equations&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-188","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/188","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=188"}],"version-history":[{"count":20,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/188\/revisions"}],"predecessor-version":[{"id":13645,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/188\/revisions\/13645"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=188"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}