Find the equation of the parabola that has zeros of x = –1 and x = 3 and a y-intercept of (0,–9). Question 1 options: A) y = 3x2 – 6x – 9 B) y = x2 – 2x + 9 C) y = 3x2 – 6x + 9 D) y = x2 – 2x – 9

A

Step-by-step explanation:

Given the zeros are x = - 1 and x = 3 then the factors are

(x + 1) and (x - 3) and the parabola is the product of the factors, that is

y = a(x + 1)(x - 3) ← where a is a multiplier

To find a substitute (0, - 9) into the equation

- 9 = a(0 + 1)(0 - 3) = a(1)(- 3) = - 3a ( divide both sides by - 3 )

3 = a, thus

y = 3(x + 1)(x - 3) ← expand the factors using FOIL

  = 3(x² - 2x - 3) ← distribute by 3

  = 3x² - 6x - 9 → A

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step-by-step explanation: