Question

The graph of a quadratic function has a vertex located at (7,-3) and passes through points (5,5) and (9,5). Which equation best represents this function?

A) f(x)=(x-7)^2-3
B) f(x)=2(x-7)^2-3
C) f(x)= -(x-5)^2+5
D) f(x)= -2(x-5)^2+5

Answer 1

B)
`f(x)=2(x-7)^2-3`.

Explanation:

The vertex form of the equation is given by
`f(x)=a(x-h)^2+k`.

We plug in the vertex to obtain:

`f(x)=a(x-7)^2-3`.

Since the graph passes through (5,5) and (9,5), they must satisfy its equation.

`5=a(9-7)^2-3`.

`5+3=4a`.

`8=4a`

Divide both sides by 4.

`a=2`

Therefore the equation is:

`f(x)=2(x-7)^2-3`.