The **x-intercept **is the point at which the given graph crosses:

the x-axis at (x, 0).

This is where** y = 0**.

The** y-intercept **is the point at which the given graph crosses:

the y-axis at (0, y).

This is where **x = 0**.

**Example**

Find the x- and y-intercepts of the graph with equation:

y = x^{2} + 4x + 3

**Answer**

We put **y = 0** to get

x^{2} + 4x + 3 = 0

Factorise to get

(x + 3) (x + 1) = 0

x = -3 or -1

So the x-intercepts are at **(-3, 0) and (-1, 0)**

We put** x = 0** to get

y = 0 + 0 + 3 = 3

So the y-intercept is **(0, 3)**

This can be checked on a graph as follows: