Q18. - Algebra 1

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 $y=-2x^2+1$

 

Step-by-Step Solution

Answer

Option D is the correct choice.

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.