{"id":186,"date":"2022-04-13T10:16:18","date_gmt":"2022-04-13T10:16:18","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=186"},"modified":"2024-08-23T17:20:31","modified_gmt":"2024-08-23T17:20:31","slug":"j-1-characteristics-of-quadratic-equations","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/j-1-characteristics-of-quadratic-equations\/","title":{"rendered":"J.1 Characteristics of quadratic equations"},"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> Characteristics of quadratic equations<\/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 has-huge-font-size wp-elements-91b61a8fb15f5033c1b27af02bd2ece2\" style=\"color:#bce711\"><strong>Quadratic Equations<\/strong><\/p>\n\n\n\n<p>A quadratic equation is a polynomial equation of degree two. It can be expressed in the general form:<\/p>\n\n\n\n<p><strong>ax\u00b2 + bx + c = 0<\/strong><\/p>\n\n\n\n<p>where a, b, and c are constants, and a \u2260 0.<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-1691e2da313cb19ff00b7d89fd9943f9\" style=\"color:#e93535\"><strong>Key Characteristics:<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Degree:<\/strong> The highest power of the variable (x) in a quadratic equation is 2.<\/li>\n\n\n\n<li><strong>Roots:<\/strong> A quadratic equation has at most two solutions, also known as roots. These roots represent the values of x that make the equation true.<\/li>\n\n\n\n<li><strong>Nature of Roots:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Real and Distinct:<\/strong> If the discriminant (b\u00b2 &#8211; 4ac) is positive, the roots are real and distinct.<\/li>\n\n\n\n<li><strong>Real and Equal:<\/strong> If the discriminant is zero, the roots are real and equal.<\/li>\n\n\n\n<li><strong>Imaginary or Complex:<\/strong> If the discriminant is negative, the roots are imaginary or complex.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Sum and Product of Roots:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Sum of Roots:<\/strong> The sum of the roots of a quadratic equation is -b\/a.<\/li>\n\n\n\n<li><strong>Product of Roots:<\/strong> The product of the roots of a quadratic equation is c\/a.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Graph:<\/strong> The graph of a quadratic equation is a parabola.\n<ul class=\"wp-block-list\">\n<li><strong>Shape:<\/strong> The shape of the parabola depends on the sign of the coefficient a.\n<ul class=\"wp-block-list\">\n<li>If a > 0, the parabola opens upward.<\/li>\n\n\n\n<li>If a &lt; 0, the parabola opens downward.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Vertex:<\/strong> The vertex of the parabola is the point where the equation changes direction.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Completing the Square:<\/strong> This is a technique used to solve quadratic equations by rewriting them in the form (x + h)\u00b2 = k.<\/li>\n\n\n\n<li><strong>Quadratic Formula:<\/strong> The quadratic formula is a general formula used to solve quadratic equations:\n<ul class=\"wp-block-list\">\n<li>x = [-b \u00b1 \u221a(b\u00b2 &#8211; 4ac)] \/ 2a<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-d72639564f6f630aa33fbd83748d77fa\" style=\"color:#f406e0\"><strong>Additional Points to Consider:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Factoring:<\/strong> In some cases, quadratic equations can be solved by factoring.<\/li>\n\n\n\n<li><strong>Discriminant:<\/strong> The discriminant (b\u00b2 &#8211; 4ac) provides information about the nature of the roots.<\/li>\n\n\n\n<li><strong>Graphing:<\/strong> Understanding the graph of a quadratic equation can help visualize the solutions.<\/li>\n\n\n\n<li><strong>Applications:<\/strong> Quadratic equations have many applications in various fields, including physics, engineering, and economics.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color wp-elements-a9ac03f52555db9773296f42b026938e\" style=\"color:#a2e604\"><strong>Upward-Facing Parabola<\/strong><\/h2>\n\n\n\n<p><strong>A parabola opens upward when the leading coefficient (a) is positive.<\/strong> This means that the quadratic term, ax\u00b2, has a positive sign.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-0c56455802b11a773d70761941ed6c86\" style=\"color:#ed9911\"><strong>Key characteristics of an upward-facing parabola:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Vertex:<\/strong> The lowest point on the parabola, also known as the minimum point.<\/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>X-intercepts:<\/strong> The points where the parabola intersects the x-axis.<\/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-f9f9ed45358bc7849249bed0e05de023\" style=\"color:#ccdd33\"><strong>Example equation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>y = x\u00b2<\/strong><\/li>\n<\/ul>\n\n\n\n<p>In this equation, the leading coefficient is 1, which is positive, resulting in an upward-facing parabola.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"640\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-1024x640.png\" alt=\"\" class=\"wp-image-13638\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-1024x640.png 1024w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-300x188.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-768x480.png 768w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-1536x960.png 1536w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-1568x980.png 1568w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image.png 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading has-text-color has-link-color wp-elements-50c8b5072e85fc949c059ed368f91156\" style=\"color:#4ac615\"><strong>Downward-Facing Parabola<\/strong><\/h2>\n\n\n\n<p><strong>A parabola opens downward when the leading coefficient (a) is negative.<\/strong> This means that the quadratic term, ax\u00b2, has a negative sign.<\/p>\n\n\n\n<p><strong>Key characteristics of a downward-facing parabola:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Vertex:<\/strong> The highest point on the parabola, also known as the maximum point.<\/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>X-intercepts:<\/strong> The points where the parabola intersects the x-axis.<\/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-aefc6b88ee96d17fef5f0f4625246e0a\" style=\"color:#2d38d1\"><strong>Example equation:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>y = -x\u00b2<\/strong><\/li>\n<\/ul>\n\n\n\n<p>In this equation, the leading coefficient is -1, which is negative, resulting in a downward-facing parabola.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"640\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-2-1024x640.png\" alt=\"\" class=\"wp-image-13640\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-2-1024x640.png 1024w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-2-300x188.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-2-768x480.png 768w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-2-1536x960.png 1536w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-2-1568x980.png 1568w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-2.png 1600w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\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-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-b09c7746ffd2e8e8cdef2fb3584c0881\" style=\"background-color:#e2bff1\"><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>Look at this graph:<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-1-1.png\" alt=\"\" class=\"wp-image-10704\" style=\"width:390px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-1-1.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-1-1-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-1-1-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-1-1-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-f01e392389479e75397bdbd4f0ea0ef6\" style=\"color:#b00012\"><strong>What are the coordinates of the vertex ?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-bd8757cbe1fb241be40a6b265b466627\">The lowest point on the graph is at(4,&nbsp;<sup>\u2013<\/sup>7).<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__3_-removebg-preview.png\" alt=\"\" class=\"wp-image-10708\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__3_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__3_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__3_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-primary-color has-text-color has-link-color wp-elements-8569ff2c1ea75fa1757f51487363ddd6\">So, the vertex is(4,&nbsp;<sup>\u2013<\/sup>7).<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-27b4500698268fbccb848ef34f6a83d9\" style=\"background-color:#e7a9a9\"><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>Look at this graph:<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-4.png\" alt=\"\" class=\"wp-image-10713\" style=\"width:416px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-4.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-4-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-4-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-4-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-f01e392389479e75397bdbd4f0ea0ef6\" style=\"color:#b00012\"><strong>What are the coordinates of the vertex ?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>The lowest point on the graph is at(0,&nbsp;0).<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__5_-removebg-preview.png\" alt=\"\" class=\"wp-image-10714\" style=\"width:518px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__5_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__5_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__5_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So,the vertex is(0,&nbsp;0).<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-955bf0b989b78b62107f6e6629700fbc\" style=\"background-color:#dca2e4\"><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>Look at this graph:<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-7.png\" alt=\"\" class=\"wp-image-10717\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-7.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-7-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-7-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1-7-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-c9a414e5f25a56c836e7b4000b8000d2\" style=\"color:#b00012\"><strong>What is the y-intercept ?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>The parabola intersects the y-axis at 0.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__8_-removebg-preview.png\" alt=\"\" class=\"wp-image-10718\" style=\"width:506px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__8_-removebg-preview.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__8_-removebg-preview-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/1__8_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>So,the y-intercept is 0.<\/p>\n<\/div><\/div>\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\/534\/213\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-48.png\" alt=\"\" class=\"wp-image-6929\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-48.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-48-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-48-150x150.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\/76711\/223\/900\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-66.png\" alt=\"\" class=\"wp-image-6930\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-66.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-66-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-66-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\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\"><\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Characteristics of quadratic equations Key Notes : Quadratic Equations A quadratic equation is a polynomial equation of degree two. It can be expressed in the general form: ax\u00b2 + bx + c = 0 where a, b, and c are constants, and a \u2260 0. Key Characteristics: Additional Points to Consider: Upward-Facing Parabola A parabola<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/j-1-characteristics-of-quadratic-equations\/\">Continue reading <span class=\"screen-reader-text\">&#8220;J.1 Characteristics of 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-186","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/186","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=186"}],"version-history":[{"count":18,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/186\/revisions"}],"predecessor-version":[{"id":13641,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/186\/revisions\/13641"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=186"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}