https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:standard-form-quadratic/v/application-problem-with-quadratic-formula 2026-06-16T15:55:43.561813682Z Quadratic word problem: ball Sal solves a word problem about a ball being shot in the air. The equation for the height of the ball as a function of time is modeled by a quadratic function. Sal Khan video https://cdn.kastatic.org/googleusercontent/dvyWuNQ8WzVeTAUzYpi9a4ZcD4dvdto9umYIzFqnduWfAOekC-W154fwNxUj9yGJzcgbX1qd08x2RY3KGj4AmPSH Quadratic word problem: ball Sal solves a word problem about a ball being shot in the air. The equation for the height of the ball as a function of time is modeled by a quadratic function. https://cdn.kastatic.org/ka-youtube-converted/OZtqz_xw0SQ.mp4/OZtqz_xw0SQ.mp4 353 Function model construction and application 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 Function model construction and application https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:standard-form-quadratic/e/key-features-quadratics 2026-06-16T15:55:43.561813682Z Quadratic word problems (standard form) Solve real-world word problems that involve quadratic models. In this exercise, the models are given in standard form. Tomer Gal exercise https://www.khanacademy.org/math/algebra-2-fl-best/x727ff003d4fc3b92:quadratic-functions/x727ff003d4fc3b92:writing-quadratic-functions/e/writing-quadratic-equations-word-problems 2026-06-26T19:21:03.457278957Z Word problems: write quadratic equations Let's try to express some real-world scenarios using quadratic equations ashish exercise https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:function-model-construction-and-application/v/constructing-rational-function-models 2026-06-26T18:30:50.997824794Z Constructing rational function models Construct a rational function model based off of inversely proportional relationships. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/c05829a6-e0b5-4524-8e38-6fb0b8b8cb85_1280_720_base.png Constructing rational function models Construct a rational function model based off of inversely proportional relationships. https://cdn.kastatic.org/ka-youtube-converted/in8QJym_rzM.mp4/in8QJym_rzM.mp4 137 Function model construction and application https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:function-model-construction-and-application/e/construct-rational-function-models 2026-06-26T19:09:02.853164112Z Construct rational function models Construct rational function models for inverse relationships from data or applications and use them to find average rates of change. Courtney Chernin-Hitchings exercise https://www.khanacademy.org/math/algebra-home/alg-functions/alg-graphing-nonlinear-piecewise-functions/v/finding-a-piecewise-function-definition-from-graph 2020-06-23T07:22:42Z Graphs of nonlinear piecewise functions Sal is given the graph of a piecewise function and several possible formulas. He determines which is the correct formula. Sal Khan video https://cdn.kastatic.org/googleusercontent/M8aZJx01n6sCbdCU2MKCKqcORF87eye1fqhnVa-TT4mTJRMlZJ4NYJs2afLXzZ61Jmt1O7XXoSTCJyQcNW4Hp7z5PA Graphs of nonlinear piecewise functions Sal is given the graph of a piecewise function and several possible formulas. He determines which is the correct formula. https://cdn.kastatic.org/ka-youtube-converted/IJWDyPFXGyM.mp4/IJWDyPFXGyM.mp4 263 Function model construction and application https://www.khanacademy.org/math/algebra-home/alg-functions/alg-graphing-nonlinear-piecewise-functions/e/graphing-piecewise-functions 2024-11-11T02:53:45.885176652Z Graphs of nonlinear piecewise functions Given the graph of a nonlinear piecewise function, find its formula. Stacy Beaudoin exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:interpreting-features-of-graphs/v/interpreting-function-graphs-word-problems 2021-05-05T14:53:17Z Graph interpretation word problem: temperature When a function models a real-world context, we can learn a lot about the content from the function's graph. In this video, we consider a graph that models temperature over time. video https://cdn.kastatic.org/googleusercontent/pWGva4CEpx3XItKT67AY_gECCYr-izrDMszsOFBPP3jLLQHndgBBPXQARYLBtlJ7yfvm5NTBqsj3yvTyAUsFYF21 Graph interpretation word problem: temperature When a function models a real-world context, we can learn a lot about the content from the function's graph. In this video, we consider a graph that models temperature over time. https://cdn.kastatic.org/ka-youtube-converted/VtBRkjRua0I.mp4/VtBRkjRua0I.mp4 235 Function model construction and application https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:functions/x2f8bb11595b61c86:interpreting-features-of-graphs/v/interpreting-features-of-functions-2-example-1 2021-05-05T14:53:17Z Graph interpretation word problem: basketball When a function models a real-world context, we can learn a lot about the context from the function's graph. In this video, we interpret the y-intercept of a graph that models a basketball free throw. Sal Khan video https://cdn.kastatic.org/googleusercontent/9stkA6gDjSfk8mIk5cruTs9opu4NLonV325tq4ID3s0gzzcaRLhcqIkjFBrbelzIY1_xUZA1fuWDrh0ziUfN5i0k Graph interpretation word problem: basketball When a function models a real-world context, we can learn a lot about the context from the function's graph. In this video, we interpret the y-intercept of a graph that models a basketball free throw. https://cdn.kastatic.org/ka-youtube-converted/M3PTPN7NH8M.mp4/M3PTPN7NH8M.mp4 230 Function model construction and application https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/applying-rational-equations-1 2021-06-29T20:27:56Z Rational equations word problem: combined rates Sal solves a word problem about the combined leaf-bagging rates of Ian and Kyandre, by creating a rational equation that models the situation. Sal Khan video https://cdn.kastatic.org/googleusercontent/YtleC_3qgEHL0HU_I_NrYrzg4VexqBWMUriZuKQhM9obdO5eCwtQgWpcnFi6tvnvewboLuMb2WDIyLssHu-ThMon Rational equations word problem: combined rates Sal solves a word problem about the combined leaf-bagging rates of Ian and Kyandre, by creating a rational equation that models the situation. https://cdn.kastatic.org/ka-youtube-converted/gD7A1LA4jO8.mp4/gD7A1LA4jO8.mp4 326 Function model construction and application https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/v/applying-rational-equations-2 2021-06-29T20:27:54Z Rational equations word problem: combined rates (example 2) Sal solves a word problem about the combined deck-staining rates of Anya and Bill, by creating a rational equation that models the situation. Sal Khan video https://cdn.kastatic.org/googleusercontent/xd7Jt9VaRGLK_25RZC_OckJ3IwnIUcB47YC831p09S0kuqAMQGT52kp58nWiJeLtfUdpisjBuqRrTcLi_rU2qE3e Rational equations word problem: combined rates (example 2) Sal solves a word problem about the combined deck-staining rates of Anya and Bill, by creating a rational equation that models the situation. https://cdn.kastatic.org/ka-youtube-converted/E1j8W64NQ0Y.mp4/E1j8W64NQ0Y.mp4 360 Function model construction and application https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:rational-functions/x9e81a4f98389efdf:modeling-with-rational-functions/e/mixtures-and-combined-rates-word-problems 2024-08-12T05:01:46.814165037Z Mixtures and combined rates word problems Determine individual rates and overall outcomes from real world contexts involving combinations of different speeds or concentrations. Charlotte Auen exercise https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:function-model-construction-and-application/v/constructing-models-of-data-sets-using-technology-and-regressions 2026-06-16T15:55:43.561813682Z Constructing models of data sets using technology and regressions Using a TI-84 to construct models of data sets. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/94e89c01-8ee4-4e0a-9527-1d8537403b9c_1280_720_base.png Constructing models of data sets using technology and regressions Using a TI-84 to construct models of data sets. https://cdn.kastatic.org/ka-youtube-converted/WDO-eotwPP8.mp4/WDO-eotwPP8.mp4 377 Function model construction and application