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

(1, 14)

Step-by-step 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).