Finding the x and y Intercepts
In order to find the x and y intercepts of a graph, we need to remember that we’re looking for where the graph crosses the x and y axes. If the graph crosses the x-axis, then that point has a y-coordinate of 0 since all points on the x-axis have y-coordinate 0. To find an x-intercept, merely substitute 0 for y, and then solve for x. If the graph crosses the y-axis, then that point has an x-coordinate of 0 since all points on the y-axis have x-coordinate 0. To find the y-intercepts, we set x equal to zero and solve for y. Thus, if 
, the y-intercept of the graph is 
. Note that we usually just say that 
is the y-intercept, rather than more accurately saying that 
is the y-intercept.
Example 1
Find the x and y intercepts of the graph of 
.
Solution1
The y-intercept is 
To find the x-intercept. Substitute 0 for y and solve for x:
The y-intercept is at the point (0, -7) and the x-intercept is ( 
, 0).
Example 2
Find the x and y intercepts of 
.
Solution 2
To find the y-intercept, we evaluate 
. So, our y-intercept is -2.
To find the x-intercept, we solve
So, our x-intercepts are 1, -2
Example 3
Find the x and y intercepts of 
Solution 3
First, we evaluate 
to see that the y-intercept is 0. Then, we solve
So, the x-intercepts are -3, 0, 5.
Example 4
Find the x and y intercepts of 
Solution 4
First, we set y equal to zero.
So, our x-intercepts are 2 and -2.
Next, we set x equal to zero.
So, our y-intercepts are 3 and -3.