{"id":204,"date":"2022-04-13T10:19:27","date_gmt":"2022-04-13T10:19:27","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=204"},"modified":"2024-08-25T07:41:59","modified_gmt":"2024-08-25T07:41:59","slug":"j-10-graph-a-quadratic-equation","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/j-10-graph-a-quadratic-equation\/","title":{"rendered":"J.10 Graph a quadratic equation"},"content":{"rendered":"\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<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Graph a quadratic equation<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-42835b82ad7e85aa797578eaf84bffc6\" style=\"color:#f08410\"><strong>Understanding Quadratic Equations and Graphs<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A quadratic equation is a polynomial equation of degree two, typically expressed in the form ax\u00b2 + bx + c = 0.<\/li>\n\n\n\n<li>The graph of a quadratic equation is a parabola, which is a U-shaped curve.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-b2ecb18825aae74b9661d95ac272bb66\" style=\"color:#149538\"><strong>Key Properties of Quadratic Graphs<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Vertex:<\/strong> The point where the parabola changes direction.<\/li>\n\n\n\n<li><strong>Axis of Symmetry:<\/strong> A vertical line that divides the parabola into two symmetrical halves.<\/li>\n\n\n\n<li><strong>Roots:<\/strong> The points where the parabola intersects the x-axis (also known as x-intercepts).<\/li>\n\n\n\n<li><strong>Y-intercept:<\/strong> The point where the parabola intersects the y-axis.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-a35a413abc35a4eb89018c9589a0eaf2\" style=\"color:#c1f027\"><strong>Steps to Graph a Quadratic Equation<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify the Vertex:<\/strong> Use the vertex formula: (-b\/2a, f(-b\/2a)) to find the coordinates of the vertex.<\/li>\n\n\n\n<li><strong>Determine the Axis of Symmetry:<\/strong> The axis of symmetry is a vertical line passing through the vertex. Its equation is x = -b\/2a.<\/li>\n\n\n\n<li><strong>Find the Roots (if any):<\/strong> Solve the quadratic equation to find the x-intercepts. You can use factoring, completing the square, or the quadratic formula.<\/li>\n\n\n\n<li><strong>Plot Key Points:<\/strong> Plot the vertex, the axis of symmetry, and any roots you found.<\/li>\n\n\n\n<li><strong>Sketch the Parabola:<\/strong> Use the shape of the parabola (upward if a &gt; 0, downward if a &lt; 0) and the plotted points to sketch the curve.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-1602a483d52a9bf6352d8c3c27f04b83\" style=\"color:#f3159e\"><strong>Example<\/strong><\/p>\n\n\n\n<p>Graph the quadratic equation f(x) = x\u00b2 &#8211; 4x + 3<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Vertex: (-b\/2a, f(-b\/2a)) = (2, -1)<\/li>\n\n\n\n<li>Axis of Symmetry: x = 2<\/li>\n\n\n\n<li>Roots: Solve x\u00b2 &#8211; 4x + 3 = 0 to find x = 1 and x = 3<\/li>\n\n\n\n<li>Sketch the parabola using the vertex, axis of symmetry, and roots.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"640\" height=\"480\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Gemini_Chart_Image_1u4l71u4l71u4l71.png\" alt=\"\" class=\"wp-image-13672\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Gemini_Chart_Image_1u4l71u4l71u4l71.png 640w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/Gemini_Chart_Image_1u4l71u4l71u4l71-300x225.png 300w\" sizes=\"auto, (max-width: 640px) 100vw, 640px\" \/><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-b5a4097c4c724b6b0e1b4510eba15d06\" style=\"color:#b5ff0a\"><strong>Additional Tips<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To get a more accurate graph, plot additional points by substituting different x-values into the equation and calculating the corresponding y-values.<\/li>\n\n\n\n<li>Consider the end behavior of the parabola: if a &gt; 0, the parabola opens upward, and if a &lt; 0, the parabola opens downward.<\/li>\n\n\n\n<li>Use graphing technology (e.g., graphing calculators or online graphing tools) to visualize the graph more easily<\/li>\n<\/ul>\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 has-background has-large-font-size\" style=\"background-color:#e1c8f1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-a89f68c9c253a0efd7e3e377991e848a\" style=\"color:#b00012\"><strong>Graph&nbsp;the function&nbsp;f(x)=6x<sup>2<\/sup>.<\/strong><\/p>\n\n\n\n<p>Plot&nbsp;the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the&nbsp;first.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9.png\" alt=\"\" class=\"wp-image-10780\" style=\"width:358px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p>To&nbsp;graph the parabola, first find the&nbsp;vertex.<\/p>\n\n\n\n<p>f(x)=6x<sup>2<\/sup><\/p>\n\n\n\n<p>=6(x\u2013<strong>0<\/strong>)<sup>2<\/sup>+<strong>0<\/strong><\/p>\n\n\n\n<p>The&nbsp;vertex is&nbsp;(<strong>0<\/strong>,<strong>0<\/strong>),&nbsp;which is the&nbsp;origin.<\/p>\n\n\n\n<p>Now&nbsp;look for another point on the parabola with integer or half-integer coordinates. One such point is&nbsp;(1\/2,3\/2).&nbsp;(Plugging in&nbsp;x=1\/2&nbsp;yields&nbsp;y=3\/2.)&nbsp;So, plot this&nbsp;point.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview.png\" alt=\"\" class=\"wp-image-10782\" style=\"width:360px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#92f1a6\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-6d3f469692b9f42cda2420cfada663c1\" style=\"color:#b00012\"><strong>Graph&nbsp;the function&nbsp;f(x)=7x<sup>2<\/sup>.<\/strong><\/p>\n\n\n\n<p>Plot&nbsp;the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the&nbsp;first.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-1.png\" alt=\"\" class=\"wp-image-10784\" style=\"width:332px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-1.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-1-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-1-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p>To&nbsp;graph the parabola, first find the&nbsp;vertex.<\/p>\n\n\n\n<p>f(x)=7x<sup>2<\/sup><\/p>\n\n\n\n<p>=7(x\u2013<strong>0<\/strong>)<sup>2<\/sup>+<strong>0<\/strong><\/p>\n\n\n\n<p>The&nbsp;vertex is&nbsp;(<strong>0<\/strong>,<strong>0<\/strong>),&nbsp;which is the&nbsp;origin.<\/p>\n\n\n\n<p>Now&nbsp;look for another point on the parabola with integer or half-integer coordinates. One such point is&nbsp;(1,7).&nbsp;(Plugging in&nbsp;x=1&nbsp;yields&nbsp;y=7.)&nbsp;So, plot this&nbsp;point.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-10785\" style=\"width:348px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-1.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-1-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#b4def3\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-46e778efe50d46be0f7b72d24ddb7c21\" style=\"color:#b00012\"><strong>Graph&nbsp;the function&nbsp;f(x)=5x<sup>2<\/sup>.<\/strong><\/p>\n\n\n\n<p>Plot&nbsp;the vertex. Then plot another point on the parabola. If you make a mistake, you can erase your parabola by selecting the second point and placing it on top of the&nbsp;first.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-2.png\" alt=\"\" class=\"wp-image-10786\" style=\"width:369px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-2.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-2-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-9-2-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div><\/div><\/div>\n\n\n\n<p>To&nbsp;graph the parabola, first find the&nbsp;vertex.<\/p>\n\n\n\n<p>f(x)=5x<sup>2<\/sup><\/p>\n\n\n\n<p>=5(x\u2013<strong>0<\/strong>)<sup>2<\/sup>+<strong>0<\/strong><\/p>\n\n\n\n<p>The&nbsp;vertex is&nbsp;(<strong>0<\/strong>,<strong>0<\/strong>),&nbsp;which is the&nbsp;origin.<\/p>\n\n\n\n<p>Now&nbsp;look for another point on the parabola with integer or half-integer coordinates. One such point is&nbsp;(1,5).&nbsp;(Plugging in&nbsp;x=1&nbsp;yields&nbsp;y=5.)&nbsp;So, plot this&nbsp;point.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-2.png\" alt=\"\" class=\"wp-image-10787\" style=\"width:368px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-2.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-2-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__11_-removebg-preview-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div><\/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\/76707\/794\/681\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-57.png\" alt=\"\" class=\"wp-image-6974\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-57.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-57-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-57-150x150.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\/76762\/014\/732\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75.png\" alt=\"\" class=\"wp-image-6975\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-75-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Graph a quadratic equation Key Notes : Understanding Quadratic Equations and Graphs Key Properties of Quadratic Graphs Steps to Graph a Quadratic Equation Example Graph the quadratic equation f(x) = x\u00b2 &#8211; 4x + 3 Additional Tips Learn with an example Graph&nbsp;the function&nbsp;f(x)=6&#215;2. Plot&nbsp;the vertex. Then plot another point on the parabola. If you make<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/j-10-graph-a-quadratic-equation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.10 Graph a quadratic equation&#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-204","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/204","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=204"}],"version-history":[{"count":21,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/204\/revisions"}],"predecessor-version":[{"id":13673,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/204\/revisions\/13673"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}