Skip to content

Physics Playground

Simulations How we teach Pricing

Language

Log in Start learning free

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

© 2026 Physics Playground. Made for the curious.Language

Exercises Polynomials and factoring

Example 8 from Algebra and Trigonometry, 5.2 Power Functions and Polynomial Functions

Determining the Intercepts of a Polynomial Function

Given the polynomial function $f (x) = (x - 2) (x + 1) (x - 4),$ written in factored form for your convenience, determine the y- and x-intercepts.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
The y-intercept occurs when the input is zero so substitute 0 for $x .$

$\begin{matrix} f (0) & = & f (0) = (0 - 2) (0 + 1) (0 - 4) \\ = & (- 2) (1) (- 4) \\ = & 8 \end{matrix}$

The y-intercept is (0, 8).

The x-intercepts occur when the output is zero.

$0 = (x - 2) (x + 1) (x - 4)$

$\begin{matrix} x - 2 & = & 0 & or & x + 1 & = & 0 & or & x - 4 & = & 0 \\ x & = & 2 & or & x & = & −1 & or & x & = & 4 \end{matrix}$
The x-intercepts are $(2, 0), (- 1, 0),$ and $(4, 0) .$
We can see these intercepts on the graph of the function shown in Figure 10.

Figure 10

How did it go?

PreviousIdentifying End Behavior and Degree of a Polynomial Function Next Determining the Intercepts of a Polynomial Function with Factoring

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 5.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.