Question

Find the vertex of this parabola.



y = -2x2 + 4x + 12

Answer 1

For this case we have the following equation:

`y = -2x ^ 2 + 4x + 12`
Deriving we have:

`y = -2x ^ 2 + 4x + 12 y '= -4x + 4`
We match zero:

`-4x + 4 = 0`
We clear the value of x:

`4x = 4 x = 4/4 x = 1`
Then, we substitute the value of x in the equation of the parabola:

`y = -2 (1) ^ 2 + 4 (1) + 12 y = -2 + 4 + 12 y = 14`
Thus, the vertex of the parabola is the ordered pair:

`(x, y) = (1, 14)`
Answer:
The vertice is:

`(x, y) = (1, 14)`