How to find a function whose graph is a parabola with vertex (-2,2) and that passes through the point (1,-4)?

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Marcelo Cisneros · Accepted Answer

The equation of a parabola in                     vertex form             is                              ∣                                                                                                                                a                      a                                                                                                            y                    =                    a                                                                  (                        x                        -                        h                        )                                            2                                        +                    k                                                                                                              a                      a                                                                                        ∣                                            ̲                                ¯                    where a is a constant and (h,k) are the vertex&#039;s coordinates.here (h ,k) = (-2 ,2) so we can write a &#039;partial&#039; equation.      ⇒    y    =    a                  (        x        +        2        )            2        +    2  To find a, substitute x = 1 , y = -4 from (1 ,-4) into the partial equation.      a                  (        1        +        2        )            2        +    2    =    -    4    ⇒    9    a    =    -    6    ⇒    a    =    -          2      3            ⇒    y    =    -          2      3                      (        x        +        2        )            2        +    2                 is the equation       graph{-2/3(x+2)^2+2 [-10, 10, -5, 5]}

How to find a function whose graph is a parabola with vertex (-2,2) and that passes through the point (1,-4)?

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