Calculus > How to Find Intercepts in Calculus

Being able to **find intercepts **in calculus is something you’ll do over and over again. Intercepts are where the function crosses the x-axis (the x-intercept) and the y-axis (the y-intercept). There are several ways you can find intercepts in calculus: the* guess and check* method, *factoring*, using the *quadratic equation*, or finding the solution using a *graphing calculator*. Guess and check works well for very simple equations like y = x + 2, but you’ll rarely be dealing with simple equations in calculus. Most graphing calculators have the ability to solve for intercepts (you can find a simple one here). However, in many cases (especially in elementary algebra or pre-calculus), you’ll need to find the solutions algebraically.

## How to Find Intercepts in Calculus: Examples

**Sample problem 1: **Find the intercepts of the function y=x^{3} – 9x.

Step 1: **Set x to 0 **in your function to find the x-intercept(s):

x^{3} – 9x = 0 x(x – 3) (x + 3) = 0, so x=0, x= -3, x =3.

Written as ordered pairs, the x-intercepts are (-3, 0), (0, 0) and (3, 0).

Step 2: **Set y to 0 **and then solve to find the y-intercept:

x^{3} – 9x = y(0)^{3} – 9(0) = y. y=0.

**Sample problem 2:** Find the intercepts of the equation x^{2} – 2x -1.

Step 1: **Set x to 0** in your function to find the x-intercept:

0^{2} – 2(0) -1 = -1.

Written as an ordered pair, the x-intercept is (0, -1).

Step 2. **Set y to 0** and then solve to find the y-intercept:

0 = x^{2} – 2x -1 (setting y to zero)

x = -1± √ 2 (using the quadratic formula to solve)

Therefore, there are two intercepts at (-1- √ 2, 0) and (-1 + √ 2, 0).

**Tip:** Check your solutions on a graphing calculator if you can, to see if they make sense. Looking at this particular graph, we can clearly see that there are two points where the graph crosses the x-axis and one point where it crosses the y = axis.

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