Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.2 - Quadratic Functions - Concept and Vocabulary Check - Page 329: 6


The difference between the two numbers is 8. If one number is represented by x, the other number can be expresses as $8-x$. The product of the numbers, $P\left( x \right)$, expressed in the form $P\left( x \right)=a{{x}^{2}}+bx+c$, is $P\left( x \right)={{x}^{2}}-8x$.

Work Step by Step

The difference between the two number is 8. It is assumed that one number is x and the other number is y. From the statement it is concluded that: $\begin{align} & x-y=8 \\ & -y=8-x \\ & y=x-8 \end{align}$ So, the other number is expressed as $8-x$. $P\left( x \right)$ is the product of the numbers; $\begin{align} & P\left( x \right)=xy \\ & =x\left( x-8 \right) \\ & ={{x}^{2}}-8x \end{align}$ So, the product of $P\left( x \right)$ is expressed in the form $P\left( x \right)=a{{x}^{2}}+bx+c$ is ${{x}^{2}}+\left( -8 \right)x$
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