Chapter 8, Problem 4CR

To determine

To graph: The quadratic function $h\left(x\right)=-6x^2$ and compare with the graph of $f\left(x\right)=x^2$ .

Explanation of Solution

Given information:

The equation of quadratic function $h\left(x\right)=-6x^2$ .

Graph:

The graph of the quadratic function $h\left(x\right)=-6x^2$ is sketched with help of ordered pairs.

Construct a table of values with values of independent and dependent variable.

For some values of x evaluate the corresponding values of the function.

  $\begin{array}{cccccc}x& -2& -1& 0& 1& 2\\ h\left(x\right)& -24& -6& 0& -6& -24\end{array}$

Plot the ordered pairs on a coordinate plane and join the points to obtain the smooth curve.

The red curve represents the quadratic function $h\left(x\right)=-6x^2$ and the blue curve represents the function $f\left(x\right)=x^2$ .

  

Interpretation:

The quadratic functions $h\left(x\right)=-6x^2$ and $f\left(x\right)=x^2$ have vertex at the origin $\left(0,0\right)$ . The axis of symmetry is the y-axis. The function $h\left(x\right)=-6x^2$ opens downward and $f\left(x\right)=x^2$ opens upward. The curve $h\left(x\right)=-6x^2$ is the reflection of the function $f\left(x\right)=x^2$ about the x-axis. The curve $g\left(x\right)=-\frac{3}{4}{x}^2$ is narrower than the function $f\left(x\right)=x^2$ as the function $h\left(x\right)=-6x^2$ is the vertical stretch of the function $f\left(x\right)=x^2$ by a factor of $6$ .