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=x3 – 9x.
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:
x3 – 9x = y(0)3 – 9(0) = y. y=0.
Sample problem 2: Find the intercepts of the equation x2 – 2x -1.
Step 1: Set x to 0 in your function to find the x-intercept:
02 – 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 = x2 – 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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