Answer: [tex]\bold{y = -\dfrac{5}{8} (x + 3) (x + 2) (x - 4)}[/tex]
Step-by-step explanation:
It is given that x = -3, x = -2, and x = 4.
Use those values to find the factors: x + 3 = 0, x + 2 = 0, and x - 4 = 0
Multiply the factors: (x + 3) (x + 2) (x - 4) = 0
This gives us the equation: y = a (x + 3) (x + 2) (x - 4)
Next, we need to solve for "a". It is given that the y-intercept = -15
Multiply the constant of each term by "a" to find the y-intercept:
a(3)(2)(-4) = -15
-24a = -15
[tex]\dfrac{-24a}{-24}=\dfrac{-15}{-24}[/tex]
[tex]a=-\dfrac{5}{8}[/tex]
Finally, rewrite the equation to include the a-value.
[tex]\large\boxed{y = -\dfrac{5}{8} (x + 3) (x + 2) (x - 4)}[/tex]
