Question

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 graph crosses the x-axis at $x=-4$ and touches (double root) at $x=5$. So the factors are $(x+4)$ and $(x-5)^2$. The function has the form:
$f(x)=a(x+4)(x-5)^2$

Step2: Solve for leading coefficient a

Use the y-intercept $(0, -300)$:
$-300=a(0+4)(0-5)^2$
$-300=a(4)(25)$
$-300=100a$
$a=\frac{-300}{100}=-3$

Step3: Write final function

Substitute $a=-3$ into the factored form:
$f(x)=-3(x+4)(x-5)^2$

Answer:

$f(x)=-3(x+4)(x-5)^2$