Question

Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.
Third-degree, with zeros of −4, −2, and 3, and a y-intercept of −13.

p(x) =

Answer 1

Okay so we need to find a polynomial, \(p(x)\) with zeroes \(x = 4, x = 2, x = -3\) with y-intercept of -13.

We know that p(x) will be some form of
\(p(x) = a(x - 4)(x - 2)(x + 3)\) right?

Answer 2

yes

Answer 3

Okay now, since the y-intercept is -13, that means the y-intercept of \(p(x)\) is the point \((0,-13)\)

In other words \(p(0) = -13\)

Answer 4

So we can plug that point in to our equation for \(p(x)\):

Answer 5

\(-13 = a(0 - 4)(0 - 2)(0+3)\)

Answer 6

Then solve for \(a\)

Answer 7

\(-13 = a(-4)(-2)(3)\)

Answer 8

a = -13/24

Answer 9

Yes, however, I meant to write \(p(x) = a(x + 4)(x + 2)(x - 3)\) so a = 13/24

Answer 10

So \(p(x) = \dfrac{13}{24}(x + 4)(x + 2)(x - 3)\)

Answer 11

wow thank you hero

Answer 12

You're welcome

Answer 13

may i ask you a question ?