Question

Which is an equation for the function shown in the graph?

A$y=-2x^2$

B$y=2x^2+1$

C$y=x^2-1$

D$y=-2x^2+1$

Short answer

Option D is the correct choice.

Step-by-step solution

Step 1. Define the standard form of the quadratic function.

A quadratic function, which is written in the form, $y=a{x}^2+bx+c$, where, $a\ne 0$ is called the standard form of the quadratic function.

Step 2. Define the graph of a function.

The graph of a function is the set of all points whose coordinates $\left(x,y\right)$ satisfy the function $y=f\left(x\right)$.

Step 3. Write an equation for the function shown in the graph.

Observe the graph shown in the figure.

The graph of the parabola opens downward, so the coefficient of $x^2$must be negative.

We can ignore the options B and C, where the coefficient of $x^2$ is positive.

The vertex of the parabola is $\left(0,1\right)$, in the option A: $y=-2x^2$, the vertex is $\left(0,0\right)$. So, option A is not the correct choice.

Option D: $y=-2x^2+1$has the vertex at $\left(0,1\right)$and it opens downward.

Therefore, option D is the correct choice.