Question

graph the parabola. identify the vertex.
$y = -4x^2$
...
choose the correct graph below.
a. b. c. d.
graphs of parabolas for options a, b, c, d are shown with coordinate grids and y-axis labeled, a and b are horizontal-like curves, c opens downward, d opens upward

Explanation:

Step1: Recall parabola vertex form

The standard vertex form of a parabola is $y = a(x-h)^2 + k$, where $(h,k)$ is the vertex.

Step2: Match given equation to vertex form

For $y = -4x^2$, this can be rewritten as $y = -4(x-0)^2 + 0$. Here, $h=0$, $k=0$, so the vertex is $(0,0)$.

Step3: Determine parabola direction

Since $a=-4 < 0$, the parabola opens downward.

Step4: Match to correct graph

A downward-opening parabola with vertex at $(0,0)$ corresponds to option C.

Answer:

C. <graph of downward-opening parabola with vertex at (0,0)>
Vertex: $(0,0)$