http://www.ck12.org Chapter 1. Functions and Graphs
x-intercepts are where functions cross thexaxis and where the height of the function is zero. They are also called
roots, solutions and zeroes of a function. They are found algebraically by settingy=0 and solving forx.
Example A
What are the zeroes andy-intercepts of the parabolay=x^2 − 2 x−3?
Solution using Graph:
The zeroes are at (-1, 0) and (3, 0). They-intercept is at (0, -3).
Solution using Algebra:
Substitute 0 foryto find zeroes.
0 =x^2 − 2 x− 3 = (x− 3 )(x+ 1 )
y= 0 ,x= 3 ,− 1
Substitute 0 forxto find they-intercept.
y= ( 0 )^2 − 2 ( 0 )− 3 =− 3
x= 0 ,y=− 3
Example B
Identify the zeroes andy-intercepts for the sine function.
Solution:They-intercept is (0, 0). There are four zeroes visible on this portion of the graph. One thing you know
about the sine graph is that it is periodic and repeats forever in both directions. In order to capture everyx-intercept,
you must identify a pattern instead of trying to write out every single one.
The visiblex-intercepts are 0,π, 2 π, 3 π. The pattern is that there is anx-intercept every multiple ofπincluding
negative multiples. In order to describe all of these values you should write:
Thex-intercepts are±nπwherenis an integer{ 0 ,± 1 ,± 2 ,...}.