How to Find The X and Y Intercepts 
The xintercepts are points where the graph of a function or an equation crosses or "touches" the xaxis of the Cartesian Plane. You may think of this as a point with yvalue of zero. 
 To find the xintercepts of an equation, let y = 0 then solve for x.
 In point notation, it is written as ( x , 0 )

xintercept of a line 
xintercepts of a parabola 


The yintercepts are points where the graph of a function or an equation crosses or "touches" the yaxis of the Cartesian Plane. You may think of this as a point with xvalue of zero. 
 To find the yintercepts of an equation, let x = 0 then solve for y.
 In point notation, it is written as ( 0 , y )

yintercept of a line 
yintercept of a parabola 





Example 1: From the graph, describe the x and y intercepts using point notation.
The graph crosses the xaxis at , therefore, we can write the xintercepts as points .
Similarly, the graph crosses the yaxis at . Its yintercept can be written as the point .
Example 2: Find the x and y intercepts of the line .
To find the xintercepts algebraically, we let y = 0 in the equation and then solve for values of x. In the same manner, to find for yintercepts algebraically, we let x = 0 in the equation and then solve for y.
xintercepts
( let y = 0, then solve for x ) 
yintercepts
( let x = 0, then solve for y) 


written as point: 
written as point: 
Here's the graph to verify that our answers are correct.
Example 3: Find the x and y intercepts of the quadratic equation .
The graph of this quadratic equation is a parabola. We expect it to have a "U" shape where it would either open up or down.
To solve for the xintercept of this problem, you will factor a simple trinomial. Then you set each binomial factor equal to zero and solve for x.
xintercepts
(let y = 0, then solve for x) 
yintercepts
(let x = 0, then solve for y) 


as points: 
as point: 
Our solved values for both x and y intercepts match with the graphical solution.

Example 4: Find the x and y intercepts of the quadratic equation .
This is an example where the graph of the equation has a yintercept but without an xintercept.
 Let's find the yintercept first because it's extremely easy! Plug in x = 0 then solve for y.
 Now for the xintercept. Plug in y = 0, and solve for x.
The square root of a negative number is imaginary. This suggests that this equation does not have an xintercept!
The graph can verify what's going on. Notice that the graph crossed the yaxis at (0,1); but never did with the xaxis.
Example 5: Find the x and y intercepts of the circle .
This is a good example to illustrate that it is possible for the graph of an equation to have xintercepts but without yintercepts.
xintercepts
(let y = 0, then solve for x) 
yintercepts
(let x = 0, then solve for y) 


as points: 
none 
When solving for y, we arrived at the situation of trying to get the square root of a negative number. The answer is imaginary, thus, no solution. That means, the equation doesn't have any yintercepts.
The graph verifies that we are right for the values of our xintercepts, and it has no yintercepts.

