Chapter 8.3, Problem 7Q

To determine

To graph: The quadratic function $g\left(x\right)=\frac{2}{5}{x}^2$ and compare with the graph of $f\left(x\right)=x^2$ .

Explanation of Solution

Given information:

The equation of quadratic function $g\left(x\right)=\frac{2}{5}{x}^2$ .

Graph:

The graph of the quadratic function $g\left(x\right)=\frac{2}{5}{x}^2$ 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.

  $\begin{array}{cccccc}x& -5& -1& 0& 1& 5\\ g\left(x\right)& 10& \frac{2}{5}& 0& \frac{2}{5}& 10\end{array}$

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

The red curve represents the quadratic function $g\left(x\right)=\frac{2}{5}{x}^2$ and the blue curve represents the function $f\left(x\right)=x^2$ .

  

Interpretation:

The quadratic functions $g\left(x\right)=\frac{2}{5}{x}^2$ and $f\left(x\right)=x^2$ have vertex at the origin $\left(0,0\right)$ . The axis of symmetry is the y-axis. Both the functions open upward. The curve $g\left(x\right)=\frac{2}{5}{x}^2$ is wider than the function $f\left(x\right)=x^2$ as the function $g\left(x\right)=\frac{2}{5}{x}^2$ is the vertical stretch of the function $g\left(x\right)=\frac{2}{5}{x}^2$ by a factor of $\frac{2}{5}$ .