Final answer:
The correct answer is option a. The vertex of the parabola is (2, 24) and it opens downward.
Step-by-step explanation:
The quadratic equation in question is y = -2x² + 8x + 16
To determine the vertex of the parabola represented by this equation, we can use the formula x = -b/2a, where a and b are coefficients of x² and x, respectively. In this case, a = -2 and b = 8. Plugging these values into the formula, we get x = -8 / (2 * -2) = 2.
To find the corresponding y-coordinate of the vertex, we substitute x = 2 back into the equation. y = -2(2)² + 8(2) + 16 = -8 + 16 + 16 = 24.
So, the vertex of the parabola is (2, 24). To determine the direction of opening, we look at the coefficient of x². Since the coefficient is negative (-2), the parabola opens downward.
The correct option is:
(a) Vertex: (2,24) Opens: Downward