Answer:
[tex]f(x)=\dfrac{1}{2}(2x-7)(x+4)(x-6)[/tex]
Step-by-step explanation:
Cubic polynomial in intercept form:
[tex]f(x)=(x-p)(x-q)(x-r)[/tex]
where p, q and r are the zeros.
Given:
- Zeros at x = -4 and x = 6
- Passes through the point (2, 36)
Substitute the zeros into the formula:
[tex]f(x)=(x-p)(x+4)(x-6)[/tex]
Substitute the point into the equation and solve for p:
[tex]\implies (2-p)(2+4)(2-6)=36[/tex]
[tex]\implies (2-p)(6)(-4)=36[/tex]
[tex]\implies -24(2-p)=36[/tex]
[tex]\implies 2-p=-\dfrac{3}{2}[/tex]
[tex]\implies p=\dfrac{7}{2}[/tex]
Therefore:
[tex]f(x)=\left(x-\dfrac{7}{2}\right)(x+4)(x-6)[/tex]
Factor out ¹/₂ from the first parentheses:
[tex]f(x)=\dfrac{1}{2}(2x-7)(x+4)(x-6)[/tex]
