For this case we have the following equation:
[tex]y = -2x ^ 2 + 4x + 12
[/tex]
Deriving we have:
[tex]y = -2x ^ 2 + 4x + 12
y '= -4x + 4[/tex]
We match zero:
[tex] -4x + 4 = 0
[/tex]
We clear the value of x:
[tex]4x = 4
x = 4/4
x = 1[/tex]
Then, we substitute the value of x in the equation of the parabola:
[tex]y = -2 (1) ^ 2 + 4 (1) + 12
y = -2 + 4 + 12
y = 14[/tex]
Thus, the vertex of the parabola is the ordered pair:
[tex](x, y) = (1, 14)[/tex]
Answer:
The vertice is:
[tex](x, y) = (1, 14)[/tex]
