Answer:
Step-by-step explanation:
1) we have to solve the associated equation
-16x^2 + 24x + 16 = 0
-2x^2 + 3x + 2 = 0
2x^2 -3x -2 = 0
Δ = 9 + 16 = 25
x1 = (3 + 5)/4= 2
x2 = (3 - 5)/4 =-1/2
the x intercepts are -1/2 and 2
2) a maximum because the parabola opens downwards (the first term is negative)
V(x) = -b/2a = -24/-32 = 3/4
V(y) = -16(9/16) + 24(3/4) + 16 = -9+18 + 16 = 25
V(3/4,25)
3) for draw a parabola is are necessary the coordinates of the vertex and of two points: one that lies to left of the vertex, and one that lies on the right to the vertex.
So we already have the necessary informations to draw it.
