Question

final alg 1 semester 1
5
katrina graphed the function f(x) on the coordinate plane.
what is the value of f(6)? enter your answer in the box.

Explanation:

Step1: Identify the function's equation

First, recognize this is a parabola with vertex at $(2,0)$. The vertex form of a parabola is $f(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex. Substitute $h=2$, $k=0$:
$f(x)=a(x-2)^2$
Use the y-intercept $(0,4)$ to find $a$:
$4=a(0-2)^2 \implies 4=4a \implies a=1$
So the function is $f(x)=(x-2)^2$

Step2: Calculate $f(6)$

Substitute $x=6$ into the function:
$f(6)=(6-2)^2$
$f(6)=4^2=16$

Answer:

16