Question

What quadratic function does the graph represent?

Answer 1

Answer:

$f(x)=-\frac{1}{3}(x-2)^2+4$,

Step-by-step explanation:

The function of the graph can be written in the vertex form as

$f(x)=a(x-h)^2+k$, where V(h,k)=V(2,4) is the vertex of the quadratic function.

We substitute the value to obtain;

$f(x)=a(x-2)^2+4$,

The point (5,1) lies on the graph so we use it to determine the value of a.

$1=a(5-2)^2+4$,

$1-4=a(3)^2$,

$-3=9a$,

$a=-\frac{1}{3}$

The required equation is

$f(x)=-\frac{1}{3}(x-2)^2+4$,