Question

What is the vertex and equation of the parabola in vertex form.

A. Vertex (5, -2) y=-2(x-5)^ 2-2
B. Vertex (5,-2) y=2 (x-5)^ 2-2
C. Vertex (-2,5)y=-2(x+2)^2-+5
D. Vertex (-2,5) y=-2(x-2)^2-+5

Answer 1

C. Vertex (-2,5)y=-2(x+2)^2-+5

Explanation:

The vertex of a parabola is where the function's absolute maximum or minimum is located, depending on the direction of the parabola. Here, we can see that the vertex is (-2,5) because the range does not exceed 5 as it's the absolute maximum.

As for the equation, we will use the equation y=a(x-h)^2+k where (h,k) is the vertex and "a" determines stretched or shrunk the parabola is horizontally. Hence, we have y=a(x+2)^2+5 as our equation so far, and since the parabola is upside down, then C is the best answer.