Question

Find the vertex of this parabola y=-2x^2+4x+12

Answer 1

(1, 14)

Explanation:

To find the vertex, complete the square.

First, factor out the leading coefficient from the first two terms:

y = -2 (x² − 2x) + 12

Now take half of the second coefficient, square it, and add and subtract the result:

(-2/2)² = 1

y = -2 (x² − 2x + 1 − 1) + 12

Factor the perfect square:

y = -2 ((x − 1)² − 1) + 12

Distribute:

y = -2 (x − 1)² + 2 + 12

y = -2 (x − 1)² + 14

So the vertex is (1, 14).