Chapter 9.3, Problem 4CYP

To determine

Find the right graph of The function $y=-3x^2+1$

Answer to Problem 4CYP

H is the correct choice.

Explanation of Solution

Given:

The function $y=-3x^2+1$

4 options are here:

Concept Used:

Find the vertex, y − intercept and at least two points on the graph, then match the correct option.

Calculation:

The function $y=-3x^2+1$

Find the vertex and the axis of symmetry:

  $\begin{array}{l}y=-3x^2+1\\ a=-3,b=0\\ x=-\frac{b}{2a}=-\frac{0}{-6}=0\\ x=0\end{array}$ $\begin{array}{l}x=0;y=?\\ y=-3x^2+1\\ y=-3·0^2+1=1\\ \text{Vertex}=(0,1)\end{array}$ Y − Intercept is $(0,1)$

The axis of symmetry is $x=0$

Find a point and reflect them across the line of symmetry.

  $\text{If}x=-1,\text{then}y=-3·{(-1)}^2+1=-3+1=-2$ .

Reflect $(-1,-2)$ over the axis of symmetry to obtain the point $(1,-2)$

$\text{Vertex}=(0,1)$ The other two points are $(-1,-2)$ and $(1,-2)$

Thus, H is the correct choice.