Write the equation of the parabola that has the vertex at point (5,0) and passes through the point (7,−2).

The vertex form of the equation of a parabola is

                     f(x) = a( x − h)^2 + k

where (h,k) is the vertex of the parabola. In this case, we are given that      (h,k) = (5,0). Hence,

                     f(x) = a( x − 5)^2 + 0

                           =a( x − 5)^2

Since we also know the parabola passes through the point (7,−2), we can solve for a because we know that f(7) = −2.

                        a( 7 − 5)^2 = -2

                           a(2)^2 = -2

                              4a = -2

                               a = -1/2

Thus, the given parabola has equation

                      f(x) = -1/2(x − 5)^2

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