Write an equation of the parabola that passes through the point (-2,1)and has x-intercepts -9 and -3.

Question

y=?

Answer 1

The general form of the parabola is ax² + bx + c.

For this parabola, the zeros (x-intercepts) are at -9 and -3.

Therefore, x + 9 = 0 and x + 3 = 0, so those are the two factors.

f(x) = a(x + 9)(x + 3). Now we can use the given ordered pair (-2,1) to solve for a. Use FOIL to expand.

f(x) = a(x² + 12x + 27)

1 = a[(-2)² + 12(-2) + 27]

1 = a(4 - 24 + 27)

1 = a(7), so a = 1/7

The equation for the parabola is 1/7(x² + 12x + 27)

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Answer 2

y = a(x + 9)(x + 3). If x = - 2 then y = 1. So, 1 = a(- 2 + 9)(- 2 + 3), a = 1/7

y = 1/7(x + 9)(x + 3)