# Finding Intercepts From an Equation

**X Intercept**: where the graph of an equation crosses the x-axis

**Y Intercept**: where the graph of an equation crosses the y-axis

To find the intercepts:

When you want the **x intercepts** (x,0):

Set y=0 then solve for x

When you want the **y intercepts** (0,y):

Set x=0 then solve for y

### Example: Find the intercepts of y = x^{2} − 4

**x intercept: set y=0**

0 = x^{2} − 4

x^{2} = 4

x = **2** or **−2**

The points are **(2,0)** and **(−2,0)**

**y intercept: set x=0**

y = 0^{2 }− 4

y = **−4**

The point is **(0,-4)**

And here is the graph of x^{2} - 4 to confirm what we found:

### Example: Find the intercepts of x^{2 }− 5x + y^{2 }+ 3y = 0

**x intercept: set y=0**

x^{2 }− 5x + 0+ 0 = 0

x(x−5) = 0

x = **0** and **5**

The points are **(0,0)** and **(5,0)**

**y intercept: set x=0**

0 − 0 + y^{2 }+ 3y = 0

y(y+3) = 0

y = **0** or **−3**

The points are **(0,0)** and **(0,−3)**

So there are a total of 3 points:

(0,0), (5,0) and (0, −3)

And here is the graph ... it's a circle!