Think & Click: Writing Quadratic Equations Using Roots and the Vertex

Now, you try. Complete the Think & Click activity by looking at the problem below, thinking about it, and then clicking on the problem to reveal the solution.

Write the equation of a quadratic function with roots at -6 and 2 and a vertex at (-2, 6).
 

Sum of the roots:
r₁ + r₂ = -6 + 2 = -4

Product of the roots:
r₁(r₂) = -6(2) = -12

f(x) = a(x² + 4x – 12)

Use the vertex (-2, 6) to find a.

6 = a((-2)² + 4(-2) – 12)
6 = a(4 – 8 – 12)
6 = a(-16)