Answer:
(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).
