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Exercises Polynomials and factoring

Example 7 from Algebra and Trigonometry, 5.1 Quadratic Functions

Finding the y- and x-Intercepts of a Parabola

Find the y- and x-intercepts of the quadratic $f (x) = 3 x^{2} + 5 x - 2.$

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
We find the y-intercept by evaluating $f (0) .$

$\begin{matrix} f (0) & = & 3 {(0)}^{2} + 5 (0) - 2 \\ = & −2 \end{matrix}$

So the y-intercept is at $(0, −2) .$

For the x-intercepts, we find all solutions of $f (x) = 0.$

$0 = 3 x^{2} + 5 x - 2$

In this case, the quadratic can be factored easily, providing the simplest method for solution.

$0 = (3 x - 1) (x + 2)$

So the x-intercepts are at $(\frac{1}{3}, 0)$ and $(- 2, 0) .$

How did it go?

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From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 5.1, 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.