[tex] \boxed{f(x)=3(x+2)(x+4)(x-3)} [/tex]
Explanation:
Since the cubic function has zeroes at:
[tex]x=-2 \\ \\ x=-4 \\ \\ x=3[/tex]
Then, we can write this function as:
[tex]f(x)=a(x-(-2))(x-(-4))(x-3) \\ \\ f(x)=a(x+2)(x+4)(x-3)[/tex]
So our goal is to find the leading coefficient [tex]a[/tex]. Since that cubic function passes through the point (4, 144), then it is true that:
[tex]f(4)=144 \\ \\ \\ So,\ plug \ these \values \ in \ the \ function: \\ \\ f(x)=a(x+2)(x+4)(x-3) \\ \\ 144=a(4+2)(4+4)(4-3) \\ \\ 144=a(6)(8)(1) \\ \\ 144=a(48) \\ \\ a=\frac{144}{48}=3[/tex]
Finally, the cubic function is:
[tex]f(x)=3(x+2)(x+4)(x-3)[/tex]
The graph is shown below. As you can see the zeroes are:
[tex](-2,0) \\ \\ (-4,0) \\ \\ (3,0)[/tex]
And the function passes through [tex](4,144)[/tex]
Learn more:
Polynomial equations: https://brainly.com/question/1831722
#LearnWithBrainly
