https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:intro-parabolas/v/parabolas-intro 2021-05-14T17:03:12Z Parabolas intro Graphs of quadratic functions all have the same shape which we call "parabola." All parabolas have shared characteristics. For example, they are all symmetric about a line that passes through their vertex. This video covers this and other basic facts about parabolas. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Parabolas intro Graphs of quadratic functions all have the same shape which we call "parabola." All parabolas have shared characteristics. For example, they are all symmetric about a line that passes through their vertex. This video covers this and other basic facts about parabolas. https://cdn.kastatic.org/ka-youtube-converted/BGz3pkoGPag.mp4/BGz3pkoGPag.mp4 494 Quadratic graph https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:intro-parabolas/e/parabolas-intro 2026-04-10T18:10:45.893296035Z Parabolas intro Make sure you understand the basic features of parabolas: vertex, axis of symmetry, intercepts, parabolas that "open up" or "open down." Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:factored-form-quadratics/v/graphing-quadratics-in-factored-form 2021-06-30T17:32:37Z Graphing quadratics in factored form An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Graphing quadratics in factored form An example for a quadratic function in factored form is y=½(x-6)(x+2). We can analyze this form to find the x-intercepts of the graph, as well as find the vertex. https://cdn.kastatic.org/ka-youtube-converted/EV57jv7JKCs.mp4/EV57jv7JKCs.mp4 363 Quadratic graph https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:factored-form-quadratics/e/graph-quadratic-functions-in-factored-form 2026-04-08T00:54:09.631945657Z Graph quadratics in factored form Graph quadratic functions that are given in factored form. For example, graph y=(x-4)(x+2). Sulinya Ramanan exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:standard-form-quadratic/v/graphing-a-parabola-using-roots-and-vertex 2021-06-30T17:32:35Z Graphing quadratics: standard form Learn how to graph any quadratic function that is given in standard form. Here, Sal graphs y=5x²-20x+15. Sal Khan video https://cdn.kastatic.org/googleusercontent/cRCnKKAjKKn3-iOi2QgaDA6zvAPnzjaC2vxXEMkYLqSqmBOmYKhQS4-c8xgz_MWVN15PIZlWRUOunkPSX74kvrAviw Graphing quadratics: standard form Learn how to graph any quadratic function that is given in standard form. Here, Sal graphs y=5x²-20x+15. https://cdn.kastatic.org/ka-youtube-converted/MQtsRYPx3v0.mp4/MQtsRYPx3v0.mp4 281 Quadratic graph https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:standard-form-quadratic/e/graphing_parabolas_0.5 2026-03-24T23:41:07.080866137Z Graph quadratics in standard form Graph quadratic functions given in the standard form ax²+bx+c. For example, graph y=5x²-20x+15. Sid Patel exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:standard-form-quadratic/v/ex3-completing-the-square 2021-06-30T17:32:40Z Finding the vertex of a parabola in standard form Sal rewrites the equation y=-5x^2-20x+15 in vertex form (by completing the square) in order to identify the vertex of the corresponding parabola. Sal Khan video https://cdn.kastatic.org/googleusercontent/wigSts0--ntP7W8-W5pW-wvBMuV6nwqB7t0bYBb0q7mTKETAJtsDEsZMGzGvwVqvw7zYQxHm1k9BRxBT8e0iTMtd Finding the vertex of a parabola in standard form Sal rewrites the equation y=-5x^2-20x+15 in vertex form (by completing the square) in order to identify the vertex of the corresponding parabola. https://cdn.kastatic.org/ka-youtube-converted/IbI-l7mbKO4.mp4/IbI-l7mbKO4.mp4 340 Quadratic graph https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:intro-parabolas/v/interpret-parabola-context 2022-09-10T01:04:29.754011735Z Interpreting a parabola in context Given a parabola that models a context, we can relate key features of the parabola — like the y-intercept, vertex, and x-intercepts — to what they represent in the given context. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/c71966ed-5a6b-4a16-a5ed-2ee3fdb0d844_1280_720_base.png Interpreting a parabola in context Given a parabola that models a context, we can relate key features of the parabola — like the y-intercept, vertex, and x-intercepts — to what they represent in the given context. https://cdn.kastatic.org/ka-youtube-converted/_Bk6XkV9O_0.mp4/_Bk6XkV9O_0.mp4 154 Quadratic graph https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:intro-parabolas/e/interpreting-parabolas 2026-04-07T23:36:17.218592739Z Interpret parabolas in context Practice determining what different features of a parabola represent in a modeling context. Jeff Dodds exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:intro-parabolas/v/interpret-a-quadratic-graph 2022-09-10T01:04:29.754011735Z Interpret a quadratic graph We can interpret what the features of a graph of a quadratic model mean in terms of a given context. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/1b6d92b8-40c3-423e-a252-ea73ea57d438_1280_720_base.png Interpret a quadratic graph We can interpret what the features of a graph of a quadratic model mean in terms of a given context. https://cdn.kastatic.org/ka-youtube-converted/Tqxu53deWCo.mp4/Tqxu53deWCo.mp4 157 Quadratic graph https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:intro-parabolas/e/interpret-quadratic-graph 2023-12-12T00:32:03.629852833Z Interpret a quadratic graph Practice interpreting what the features of a graph representing a quadratic relationship mean in terms of a given context. Jeff Dodds exercise