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In Exercises 59-64, use a graphing utility to graph the quadratic function. Find the -intercepts of the graph and compare them with the solutions of the corresponding quadratic equation when $ f(x) = 0 $.

$ f(x) = x^2 - 8x - 20 $

$x$ -intercepts: $(-2,0) \quad(10,0)$

Algebra

Chapter 2

Polynomial and Rational Functions

Section 1

Quadratic Functions and Models

Quadratic Functions

Complex Numbers

Polynomials

Rational Functions

Campbell University

Oregon State University

Baylor University

Lectures

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In mathematics, the absolu…

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In Exercises 59-64, use a …

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In Exercises $79-84,$ find…

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Graph the function. Be sur…

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Let's go ahead and graph F in our graphing calculator. So here's F and it's graft over here and read. And also we can see the ex intercepts on the graph negative to in ten. So that should say, ex intercepts. X equals minus two and ten. Or, if you'd like to be more precise, you Khun, say negative two zero or ten zero. Now this is from the graph and let's go out and verify this algebraic lee by setting our F equals zero. So here's F and said that equal to zero and then solve for X. So there are many ways to solve this. One way is to notice that you can factor the left hand side so this certain that shouldn't be a six. Here, we can do X minus ten and then X plus two. So if you go ahead and foil this out, we'LL do that. Together you get X square plus two X minus ten x minus twenty. And if you simplify these middle terms, you get negative. Eight x So this equation here means one of two things here that X minus ten zero or X plus two zero equivalently. You can solve each of these last two equations for X to get X equals ten or X equals minus two just And so this is the algebraic verification over here on the right side of the ex intercepts that we obtained from the graphing calculator.

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