Chapter 8, Problem 27CR

To determine

To graph: The quadratic function using zeros.

Explanation of Solution

Given information: The cubic function $f(x)=2x^3-18x$

Graph:

Let’s factor and find the x intercepts to draw approximate graph

x intercept is when y or f(x) is 0

  $2x^3-18x=0$

Factor using GCF method first

  $2x(x^2-9)=0$

Factor it further using difference of squares.

  $2x(x+3)(x-3)=0$

Using zero product property

  $\begin{array}{l}2x=0\\ x+3=0\\ x-3=0\end{array}$

Solve each equation for ‘ x’ .

  $\begin{array}{l}x=0\\ x=-3\\ x=3\end{array}$

There are three x intercepts. They are (0, 0) , (-3, 0) and (3, 0).

Now, the leading coefficient is positive 2, so left end goes down and right end goes up.

  

Interpretation: The cubic function has three x intercepts and left end goes down and right end goes up.