Respuesta :

yuanhaoli66

Answer:

y = (x - 2)(x + 1)(x + 3)

Step-by-step explanation:

horizontal intercepts at x = 2, -1, -3

->  y = 0 when x = 2, x = -1, and x = -3

Think x minus what equals y?

1. y is 0 and x is 2 -> 0 = (2 - 2) -> y = (x - 2)

2. y is 0 and x is -1 -> 0 = (-1 - (-1)) -> y = (x + 1)

3. y is 0 and x is -3 -> 0 = (-3 - (-3)) -> y = (x - 3)

so the equation is y = (x - 2)(x + 1)(x + 3)

since y = 0 when x = 2, x = -1, and x = -3

facundo3141592

We want to find a polynomial given that we know its roots.

We will get:

p(x) = x^3 + 2*x^2 - 5*x - 6

-------------------------------------

A polynomial with the roots {x₁, x₂, ..., xₙ} and a leading coefficient A, we can write it as:

p(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)

Here we know that the roots (horizontal intercepts) are {2, -1 , -3} but we do not know the leading coefficient, so we will use A = 1.

Then the polynomial is:

p(x) = (x - 2)*(x + 1)*(x + 3)

Expanding that we get:

p(x) = (x^2 - x - 2)*(x + 3)

p(x) = x^3 + 2*x^2 - 5*x - 6

This is a possible equation for the polynomial with the given horizontal intercepts.

If you want to learn more, you can read:

https://brainly.com/question/11536910

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