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/touches the x-axis at $x=-6$, $x=-4$, and $x=8$. So we can write the function in factored form as $f(x)=a(x+6)(x+4)(x-8)$, where $a$ is a leading coefficient to be found.

Step2: Use y-intercept to find $a$

The y-intercept is $(0,1000)$. Substitute $x=0$, $f(x)=1000$ into the function:
$$1000 = a(0+6)(0+4)(0-8)$$
Calculate the right-hand side:
$$1000 = a(6)(4)(-8) = a(-192)$$
Solve for $a$:
$$a = \frac{1000}{-192} = -\frac{125}{24}$$

Step3: Write final function

Substitute $a$ back into the factored form.

Answer:

$f(x) = -\frac{125}{24}(x+6)(x+4)(x-8)$