Question

Write the equation of the quadratic function with roots -1 and 1 and a vertex at (0, -3).

Answer 1

So, we're trying to find f(x) = ax^2+bx+c. We have 3 unknowns which means we need to find three equations that can can derived from the problem given.

First, note that f(-1) = 0, or a(-1)^2 + b(-1) + c = 0

This reduces to: a - b + c = 0.

Second, f(1) = 0, or a(1)^2 + b(1) + c = 0

This reduces to: a + b + c = 0

Third, f(0) = -3, or a(0)^2 + b(0) + c = -3

This reduces to c = -3

Let's put them all together:

a - b + c = 0
a + b + c = 0
c = -3

Three equations for three unknowns. Solve the system of equations however you see fit.

Note that other approaches could have been used, e.g., vertex's x-component is equal to -b/(2a) = 0 -> b = 0.