Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 3 - Quadratic Functions - Review Exercises and Problems for Chapter Three - Page 130: 25

Answer

i) Zeros: $x=6$ and $x=-4$ ii) Axis of symmetry: $x= 1$ iii) Vertex: $(1,-7.5)$

Work Step by Step

The function can be written in factored form as follows. $$ \begin{aligned} y & =0.3 x^2-0.6 x-7.2 \\ & =0.3\left(x^2-2 x-24\right) \\ & =0.3(x-6)(x+4) \end{aligned} $$ Therefore, the zeros are at $x=6$ and $x=-4$.The axis of symmetry is midway between the zeros, so its equation is $x =\frac{6-4}{2}= 1$. substituting $x=1$ into $y$ gives $y=0.3(1-6)(1+4)=-7.5$.
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