Question

tinjiuh bseibhu
answer attempt 1 out of 2
$f(x) = \square$
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Explanation:

Step1: Identify roots and vertex

Roots (x-intercepts): $x=-3$, $x=2$; Vertex (minimum): $(0, -30)$

Step2: Write factored quadratic form

$f(x)=a(x+3)(x-2)$

Step3: Solve for $a$ using vertex

Substitute $(0,-30)$: $-30=a(0+3)(0-2)$
$-30=a(3)(-2) \implies -30=-6a \implies a=5$

Step4: Expand to standard form

$f(x)=5(x^2+x-6)=5x^2+5x-30$
Verify with left vertex $(-3,0)$: $5(-3)^2+5(-3)-30=45-15-30=0$, correct.

Answer:

$5x^2+5x-30$