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:
 $(x, y) = (1, 14)$