# For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at x = −2, x = 1, and x = 3.

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at $x=-2,$ $x=1$, and $x=3$. y-intercept at $\left(0,-4\right)$.

You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Demi-Leigh Barrera

Data: $x-intercept=-2,1,3$
$x-\text{intercept of multiplicity}=-4$
Degree=4
Since it is a third degree function with three x intercepts, its general equation becomes: $f\left(x\right)=a\left(x+2\right)\left(x—1\right)\left(x-3\right)$
In order to evaluate a, use the y - intercept (0,-4), therefore substitute $f\left(0\right)=-4$ in this equation:
$-4=a\left(0+2\right)\left(0—1\right)\left(0-3\right)$
Simplify: $-4=6a$
Evaluate a: $a=-\frac{4}{6}=-\left(\frac{2}{3}\right)$
This implies that the equation of the given polynomial function is $f\left(x\right)=$
$\left(-\left(\frac{2}{3}\right)\right)\left(x+3\right)\right)\left(x—1\right)\left(x-3\right)$