Question

Use the provided information to write the standard form equation of the parabola.

Opens up or down, and passes through (8,0), (13,-5), and (12,0)

Answer 1

f(x) = -x² + 20x - 96

Explanation:

Parabola f(x) = ax² + bx + c passing through points (8,0) and (12,0) means that 8 and 12 are its root and (x-8) and (x-12) are its factors

So we get:

f(x) = a(x - 8)(x - 12)

The parabola passes through point (13, -5) that means if x=13 then f(x)=-5

So:

-5 = a(13 - 8)(13 - 12)

-5 = a(5)(1)

-5 = 5a

a = -1 {<0 so parabola opens down}

Therefore:

f(x) = -(x - 8)(x - 12)

And expanding:

f(x) = -(x² - 12x - 8x + 96)

So the standard form equation of the parabola:

f(x) = -x² + 20x - 96