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

##### 1 Answer

Jun 7, 2015

Equation:

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

x of vertex:

Product of roots:

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.