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 functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:intro-parabolas/e/parabolas-intro 2026-04-15T14:40:40.016885978Z 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: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 functions 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: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 functions 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 functions 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:quadratic-forms-features/v/rewriting-a-quadratic-function-to-find-roots-and-vertex 2021-06-30T17:32:36Z Forms & features of quadratic functions Different forms of quadratic functions reveal different features of those functions. Here, Sal rewrites f(x)=x²-5x+6 in factored form to reveal its zeros and in vertex form to reveal its vertex. Sal Khan video https://cdn.kastatic.org/googleusercontent/IYWi7RoLLOMjWtLJvwRZz3CEG3Bma-p6nwFbm1bb8Ss8LqTcIrbzl4eyR9bkXrWuuliJKoYMAKpXggGwpvRUgVD- Forms & features of quadratic functions Different forms of quadratic functions reveal different features of those functions. Here, Sal rewrites f(x)=x²-5x+6 in factored form to reveal its zeros and in vertex form to reveal its vertex. https://cdn.kastatic.org/ka-youtube-converted/4Bc5-HRop5Y.mp4/4Bc5-HRop5Y.mp4 509 Quadratic functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/v/strategy-with-forms-of-quadratics 2022-10-06T23:01:00.745424633Z Worked examples: Forms & features of quadratic functions Choosing whether factored form, vertex form or standard form of a quadratic is best in different situations. video https://cdn.kastatic.org/ka_thumbnails_cache/e725d6d8-0971-44b2-82c9-a4901522cedb_1280_720_base.png Worked examples: Forms & features of quadratic functions Choosing whether factored form, vertex form or standard form of a quadratic is best in different situations. https://cdn.kastatic.org/ka-youtube-converted/eRbgHCaWQQE.mp4/eRbgHCaWQQE.mp4 402 Quadratic functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/e/identifying-and-using-quadratic-forms 2023-12-12T00:32:03.629852833Z Features of quadratic functions: strategy Identify the form of a quadratic function that immediately reveals a given feature of that function. Features in question are the y-intercept of the graph, the zeroes ("roots") of the function, and the vertex of the parabola. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/v/finding-features-of-quadratic-functions 2022-10-06T23:01:00.745424633Z Finding features of quadratic functions Sal finds the zeros, the vertex, & the line of symmetry of quadratic functions given in vertex form, factored form, & standard form. video https://cdn.kastatic.org/ka_thumbnails_cache/20ca5e7a-7f75-41ef-8bf4-7e86045363fa_1280_720_base.png Finding features of quadratic functions Sal finds the zeros, the vertex, & the line of symmetry of quadratic functions given in vertex form, factored form, & standard form. https://cdn.kastatic.org/ka-youtube-converted/V-BAdpvejTw.mp4/V-BAdpvejTw.mp4 503 Quadratic functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/e/graphing_parabolas_2 2026-03-24T23:41:07.080866137Z Graph parabolas in all forms Graph quadratic functions given in any form. Sid Patel exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/v/interpret-quadratic-models-factored-form 2022-09-10T01:04:29.754011735Z Interpret quadratic models: Factored form Given a quadratic function that models a relationship, we can rewrite the function to reveal certain properties of the relationship. Factored form helps us identify the x-intercepts or zeros of the function. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/93772e35-6d9b-4087-b53e-9b0f03fbd865_1280_720_base.png Interpret quadratic models: Factored form Given a quadratic function that models a relationship, we can rewrite the function to reveal certain properties of the relationship. Factored form helps us identify the x-intercepts or zeros of the function. https://cdn.kastatic.org/ka-youtube-converted/ITBRCLusU1s.mp4/ITBRCLusU1s.mp4 240 Quadratic functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/v/interpret-quadratic-models 2022-09-10T01:04:29.754011735Z Interpret quadratic models: Vertex form Given a quadratic function that models a relationship, we can rewrite the function to reveal certain properties of the relationship. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/e268af1e-4465-43ff-ab14-bddce8f28f96_1280_720_base.png Interpret quadratic models: Vertex form Given a quadratic function that models a relationship, we can rewrite the function to reveal certain properties of the relationship. https://cdn.kastatic.org/ka-youtube-converted/JdWEdb90V1s.mp4/JdWEdb90V1s.mp4 353 Quadratic functions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:quadratic-forms-features/e/interpreting-quadratic-models 2025-12-04T14:30:43.376793863Z Interpret quadratic models Given a quadratic function that models a relationship, rewrite the function to reveal properties of the relationship. Jeff Dodds exercise