Chapter 8, Problem 1CR

To determine

To graph: The quadratic function $p\left(x\right)=7x^2$ and compare with the graph of $f\left(x\right)=x^2$ .

Explanation of Solution

Given information:

The equation of quadratic function $p\left(x\right)=7x^2$ .

Graph:

The graph of the quadratic function $p\left(x\right)=7x^2$ 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.

  $\begin{array}{cccccc}x& -2& -1& 0& 1& 2\\ p\left(x\right)& 28& 7& 0& 7& 28\end{array}$

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

The red curve represents the quadratic function $p\left(x\right)=7x^2$ and the blue curve represents the function $f\left(x\right)=x^2$ .

  

Interpretation:

The quadratic functions $p\left(x\right)=7x^2$ 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 $p\left(x\right)=7x^2$ is narrower than the function $f\left(x\right)=x^2$ as the function $p\left(x\right)=7x^2$ is the vertical stretch of the function $f\left(x\right)=x^2$ by a factor of 7.