https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:transform-quadratic-functions/v/shifting-and-scaling-parabolas 2020-12-28T16:56:56Z Intro to parabola transformations Sal discusses how we can shift and scale the graph of a parabola to obtain any other parabola, and how this affects the equation of the parabola. Sal Khan video https://cdn.kastatic.org/googleusercontent/ospzQQp01E5WLNQf0eRF5tfoGKLcxkp4iLMdevZPRhsOwt9jBImlY9EmQbB_tQVp3Eat_1xTEh_zuxc6x9QmUlU Intro to parabola transformations Sal discusses how we can shift and scale the graph of a parabola to obtain any other parabola, and how this affects the equation of the parabola. https://cdn.kastatic.org/ka-youtube-converted/99v51U3HSCU.mp4/99v51U3HSCU.mp4 481 Transformación de funciones https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:transform-quadratic-functions/v/example-translating-parabola 2020-12-28T16:56:57Z Shifting parabolas The graph of y=(x-k)²+h is the resulting of shifting (or translating) the graph of y=x², k units to the right and h units up. For example, y=(x-3)²-4 is the result of shifting y=x² 3 units to the right and -4 units up, which is the same as 4 units down. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Shifting parabolas The graph of y=(x-k)²+h is the resulting of shifting (or translating) the graph of y=x², k units to the right and h units up. For example, y=(x-3)²-4 is the result of shifting y=x² 3 units to the right and -4 units up, which is the same as 4 units down. https://cdn.kastatic.org/ka-youtube-converted/ZmVOR6n_fzY.mp4/ZmVOR6n_fzY.mp4 282 Transformación de funciones https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:transform-quadratic-functions/e/shift-parabolas 2023-12-12T00:32:03.629852833Z Shift parabolas We can shift a parabola by moving it up, down, left, or right. Practice how this is expressed graphically and algebraically. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:transform-quadratic-functions/v/scaling-and-reflecting-parabolas 2020-12-28T16:56:57Z Scaling & reflecting parabolas The graph of y=k⋅x² is the graph of y=x² scaled by a factor of |k|. If k<0, it's also reflected (or "flipped") across the x-axis. In this worked example, we find the equation of a parabola from its graph. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Scaling & reflecting parabolas The graph of y=k⋅x² is the graph of y=x² scaled by a factor of |k|. If k<0, it's also reflected (or "flipped") across the x-axis. In this worked example, we find the equation of a parabola from its graph. https://cdn.kastatic.org/ka-youtube-converted/AMsbZLxd3lE.mp4/AMsbZLxd3lE.mp4 285 Transformación de funciones https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:transform-quadratic-functions/e/stretch-and-shrink-parabolas 2023-12-12T00:32:03.629852833Z Scale & reflect parabolas We can make parabolas wider or narrower, and we can reflect them over the $x$-axis. Practice how this is done, graphically and algebraically. Tomer Gal exercise