Question

What is the equation for the quadratic function with roots -10 and -8 and a vertex at (-9, -3).

Answer 1

Equation with roots -10 and -8 is: y = a(x + 10)(x + 8) = a(x^2 + 18x + 80) = ax^2 + 18ax + 80a . . . . . . . . (1)
Equation with vertex at (-9, -3) is y = a(x + 9)^2 - 3 = a(x^2 + 18x + 81) - 3 = ax^2 + 18ax + 81a - 3 . . . . . . . . (2)
From (1) and (2), we have
80a = 81a - 3
a = 3

Therefore, required equation is:
y = 3x^2 + 18(3)x + 80(3) = 3x^2 + 54x + 240