Question

For the following exercise, use the given information about the

polynomial graph to write the equation. Degree 3. Zeros at x=4 and
x=3. y-intercept at (0,-24).

Answer 1

To find the equation of the polynomial graph with a degree of 3, zeros at x=4 and x=3, and a y-intercept at (0, -24), we can start by writing it in factored form using the zeros and then solve for the missing value of k.

Step-by-step explanation:

The given information states that the polynomial graph has a degree of 3 and zeros at x = 4 and x = 3. Additionally, it has a y-intercept at (0, -24). To find the equation of the polynomial, we can start by writing it in factored form using the zeros:

(x - 4)(x - 3)(x - k)

Next, we can use the y-intercept to find the value of k. Since the y-intercept is (0, -24), we can set x = 0 and solve for y:

-24 = (0 - 4)(0 - 3)(0 - k)

-24 = -12(0 - k)

-24 = 12k

k = -2

Therefore, the equation of the polynomial graph is:

y = (x - 4)(x - 3)(x - (-2))

Simplifying this, we get:

y = (x - 4)(x - 3)(x + 2)