# How do you write the equation of the quadratic function with roots -1 and -7 and a vertex at (-4, 7)?

Jun 7, 2015

Equation:
f(x) = ax^2 + bx + c. Find a, b, and c

x of vertex: $x = \frac{- 1 - 7}{2} = - 4$ --> -b/2a -> b = 8a

Product of roots: $\left(a . c\right) = 7 \to c = \frac{7}{a}$

Sum of roots: -b = (- 1 - 7) = -8 -> b = 8 --> a = 1 --> c = 7

f(x) = x^2 + 8x + 7.

Check by finding the 2 real roots. Since a - b + c = 0, one real root is (-1) and the other is (-c/a = -7). Correct.