Which quadratic function, in vertex form, can be represented by the graph?

2/5/2021

Which quadratic function in vertex form can be represented by the graph that has a vertex at (3, -7) and passes through the point (1, -10)?

f(x) = a(x - h)² + k is vertex form
(h,k) are the coordinates of the vertex

Substitute (3,-7)in for h and k, and substitute (1,-10) in for x and y, in order to determine what a is.

-10 = a(1 - 3)² + (-7) {substituted vertex and x,y coordinates in}
-10 = a(-2)² - 7 {subtracted in parentheses}
-10 = 4a - 7 {squared the -2}
-3 = 4a {added 7 to each side}
a = -3/4 {divided each side by -3}

Substitute -3/4 back in for a, along with 3 for h, and -7 for k, into vertex form.

f(x) = (-3/4)(x - 3)² - 7 {substituted back into vertex form}