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Pls find equation of parabola

Pls find equation of parabola-example-1

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7 votes

Answer:

y = - 3x² + 6x + 9

Explanation:

given the zeros of a parabola x = a , x = b , then the factors are

(x - a) , (x - b)

here the zeros are x = - 1 and x = 3 , then

factors are (x + 1) and (x - 3)

the equation of the parabola is then the product of the factors, that is

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

to find a substitute the point (0, 9 ) into the equation

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

- 3 = a

then equation is

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

= - 3(x² - 2x - 3) ← distribute parenthesis by - 3

y = - 3x² + 6x + 9

User Auria
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