Question

Write the equation polynomial whose graph contains the points (1,0),(-5,0),(-2,0),(-4,30)

Answer 1

Answer:

y = 3(x - 1)(x + 5)(x + 2)

Step-by-step explanation:

Given points:   (1, 0)   (-5, 0)   (-2, 0)   (-4, 30)

x-intercepts are when y = 0

Therefore, the x-intercepts are x = 1, x = -5 and x = -2

So (x - 1), (x + 5) and (x + 2) are all factors of the polynomial.

Therefore, the equation of the polynomial is:

y = a(x - 1)(x + 5)(x + 2)  where a is a constant to be found

To find the constant a, input the point (-4, 30) into the equation and solve:

⇒ a(-4 - 1)(-4 + 5)(-4 + 2) = 30

⇒ a(-5)(1)(-2) = 30

⇒ 10a = 30

⇒ a = 3

Therefore, the equation of the polynomial is:

y = 3(x - 1)(x + 5)(x + 2)