Chapter 9.8, Problem 25HP

To determine

To calculate: To sketch the graph of a quadratic function that has x-intercept at $2$ and $6$ .

Explanation of Solution

Given information: A quadratic function that has x-intercept at $2$ and $6$

Formula Used:

A quadratic equation with x-intercepts at $a$ and $b$ is given as

  $y=\left(x-a\right)\left(x-b\right)$

Calculation:

Given a quadratic function that has x-intercept at $2$ and $6$

Thus, quadratic equation is given as

  $\begin{array}{l}y=\left(x-2\right)\left(x-6\right)\\ y=x^2-2x-6x+12\\ y=x^2-8x+12\end{array}$

Now, in order to graph the equation, let’s find the points on the graph

When $x=0$

  $\begin{array}{l}y=\left(0-2\right)\left(0-6\right)\\ y=12\end{array}$

When $y=0$

  $\begin{array}{l}\left(x-2\right)\left(x-6\right)=0\\ x=2,6\end{array}$

Plotting the points on graph:

  

Conclusion:

Hence, graph is plotted