Question

Which of the following does not accurately describe the graph $\mathit{y}\mathbf{=}\mathbf{-}\mathbf{2}{\mathit{x}}^2\mathbf{+}\mathbf{4}$?

$\mathit{A}$The parabola is symmetric about the y-axis.

$\mathit{B}$The parabola opens downward.

$\mathit{C}$The parabola has the origin as its vertex.

$\mathit{D}$The parabola crosses the x-axis in two different places.

Short answer

A statement the parabola has the origin as its vertex does not accurately describe the graph.

Step-by-step solution

Step 1. Parabola.

Parabola is a curve which is symmetric about central line, that is, axis of symmetry and the axis of symmetry intersects the parabola at only one point called vertex.

Step 2. Graph the function.

Graph the given function.

Step 3. Write a conclusion.

From the graph, it can be observed that the parabola opens downward, the parabola is symmetric about the $y$-axis, the parabola crosses the$x$-axis in two different places and the vertex of parabola is at$(0,4)$.

Therefore, the statement the parabola has the origin as its vertex does not accurately describe the graph. Option$C$is the required answer.