Question

11-12 find a formula for the quadratic function shown.
11.
12.
(4, 2)

Explanation:

Step1: Use vertex form of quadratic

The vertex form of a quadratic function is $f(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex. From the graph, the vertex is $(3,0)$, so substitute $h=3$, $k=0$:
$f(x)=a(x-3)^2$

Step2: Solve for $a$ using point $(4,2)$

Substitute $x=4$, $f(x)=2$ into the equation:
$2=a(4-3)^2$
Simplify: $2=a(1)^2 \implies a=2$

Step3: Verify with y-intercept (optional check)

Substitute $x=0$ into $f(x)=2(x-3)^2$:
$f(0)=2(0-3)^2=2\times9=18$, which matches the y-intercept on the graph.

Answer:

$f(x)=2(x-3)^2$ (or expanded form: $f(x)=2x^2-12x+18$)