Question

write a function in any form that would match the graph shown below.
answer
attempt 1 out of 2
$f(x) = $

Explanation:

Step1: Identify x-intercepts

The x-intercepts are $x=-2$ and $x=5$, so the factored form is $f(x)=a(x+2)(x-5)$.

Step2: Use y-intercept to find a

The y-intercept is $(0,30)$. Substitute $x=0, f(x)=30$:
$30=a(0+2)(0-5)$
$30=a(2)(-5)$
$30=-10a$
$a=\frac{30}{-10}=-3$

Step3: Expand to standard form (optional)

$f(x)=-3(x+2)(x-5)$
$f(x)=-3(x^2-5x+2x-10)$
$f(x)=-3(x^2-3x-10)$
$f(x)=-3x^2+9x+30$

Answer:

$f(x)=-3(x+2)(x-5)$ or $f(x)=-3x^2+9x+30$