Section 3: Zeros of the Quadratic

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Section 5.3 Zeros of the Quadratic 461 Version: Fall 2007 5.3 Zeros of the Quadratic We’ve seen how vertex form and intelligent use of the axis of symmetry can help to draw an accurate graph of the quadratic function defined by the equation f ( x ) = ax 2 + bx + c . When drawing the graph of the parabola it is helpful to know where the graph of the parabola crosses the x -axis. That is the primary goal of this section, to find the zero crossings or x -intercepts of the parabola. Before we begin, you’ll need to review the techniques that will enable you to factor the quadratic expression ax 2 + bx + c . Factoring ax 2 + bx + c when a = 1 Our intent in this section is to provide a quick review of techniques used to factor quadratic trinomials. We begin by showing how to factor trinomials having the form ax 2 + bx + c , where the leading coefficient is a = 1; that is, trinomials having the form x 2 + bx + c . In the next section, we will address the technique used to factor ax 2 + bx + c when a Ó = 1. Let’s begin with an example. Example 1. Factor x 2 + 16 x 36 . Note that the leading coefficient, the coefficient of x 2 , is a 1. This is an impor- tant observation, because the technique presented here will not work when the leading coefficient does not equal 1. Note the constant term of the trinomial x 2 + 16 x 36 is 36. List all integer pairs whose product equals 36. 1, 36 1, 36 2, 18 2, 18 3, 12 3, 12 4, 9 4, 9 6, 6 6, 6 Note that we’ve framed the pair 2, 18. We’ve done this because the sum of this pair of integers equals the coefficient of x in the trinomial expression x 2 + 16 x 36. Use this framed pair to factor the trinomial. x 2 + 16 x 36 = ( x 2)( x + 18) It is important that you check your result. Use the distributive property to multiply. ( x 2)( x + 18) = x ( x + 18) 2( x + 18) = x 2 + 18 x 2 x 36 = x 2 + 16 x 36 Copyrighted material. See: http://msenux.redwoods.edu/IntAlgText/ 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
462 Chapter 5 Quadratic Functions Version: Fall 2007 Thus, our factorization is correct. Let’s summarize the technique. Algorithm. To factor the quadratic x 2 + bx + c , proceed as follows: 1. List all the integer pairs whose product equals c . 2. Circle or frame the pair whose sum equals the coefficient of x , namely b . Use this pair to factor the trinomial. Let’s look at another example. Example 2. Factor the trinomial x 2 25 x 84 . List all the integer pairs whose product is 84. 1, 84 1, 84 2, 42 2, 42 3, 28 3, 28 4, 21 4, 21 6, 14 6, 14 7, 12 7, 12 We’ve framed the pair whose sum equals the coefficient of x , namely 25. Use this pair to factor the trinomial. x
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 12

Section 3: Zeros of the Quadratic - Section 5.3 Zeros of...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online