Question

find a formula for the quadratic function whose graph is shown.
f(x) =
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Explanation:

Step1: Identify vertex form

Quadratic vertex form: $f(x)=a(x-h)^2+k$
Vertex $(h,k)=(4,0)$ (x-intercept/vertex), so $f(x)=a(x-4)^2$

Step2: Solve for $a$ using $(5,2)$

Substitute $x=5, f(x)=2$:
$2=a(5-4)^2$
$2=a(1)^2 \implies a=2$

Step3: Expand to standard form (optional, vertex form is valid)

$f(x)=2(x-4)^2 = 2(x^2-8x+16) = 2x^2-16x+32$

Answer:

$f(x)=2(x-4)^2$ or $f(x)=2x^2-16x+32$