Question

Determine the vertex and direction of opening of the parabola for the following quadratic equation:

y = - 2x² +8x + 16
a.) Vertex: (2,24) Opens: Downward
b.) Vertex: (2,24) Opens: Upward

Answer 1

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