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

Answer:

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

Step-by-step 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:

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