1.1. Equations and Graphs http://www.ck12.org
Solution:
Find the four intercepts, by settingx=0 and solving fory, and then settingy=0 and solving forx.
Example 5:
The third equation from Example 2 is an example of a polynomial relationship. Can you find the intercepts
analytically?
Solution:
We can find thex−intercepts analytically by settingy=0 and solving forx.So, we have
x^3 − 9 x= 0
x(x^2 − 9 ) = 0
x(x− 3 )(x+ 3 ) = 0
x= 0 ,x=− 3 ,x= 3.Thex−intercepts are located at(− 3 , 0 ),( 0 , 0 ),and( 3 , 0 ).Note that( 0 , 0 )is also they−intercept. They−intercepts
can be found by settingx=0. So, we have
x^3 − 9 x=y
( 0 )^3 − 9 ( 0 ) =y
y= 0.Sometimes we wish to look at pairs of equations and examine where they have common solutions. Consider the
linear and quadratic graphs of the previous examples. We can sketch them on the same axes:
We can see that the graphs intersect at two points. It turns out that we can solve the problem of finding the points of
intersections analytically and also by using our graphing calculator. Let’s review each method.