Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 5 Polynomials and Polynomial Functions - 5.9 Write Polynomial Functions and Models - 5.9 Exercises - Skill Practice - Page 397: 18

Answer

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Work Step by Step

The standard form of the equation is: $y=ax^2+bx+c$ For $f(1)=0 \rightarrow 0=a(1)^2+b(1)+c$ For $f(2)=-3 \rightarrow -3=a(2)^2+b(2)+c$ For $f(3)=-8 \rightarrow -8=a(3)^2+b(3)+c$ We have the system: $a+b+c=0\\4a+2b+c=-3\\9a+3b+c=-8$ Multiply the first equation by $-1$ and add it to the second equation $3a+b=-3$ (1) Multiply the first equation by $-1$ and add it to the third equation $8a+2b=-8\\ \rightarrow 4a+b=-4$ We have the new system: $a+b+c=0\\3a+b=-3\\4a+b=-4$ Multiply the second new equation by $-1$ and add it to the third equation: $a=-1$ Find $b$: $3(-1)+b=-3\\ \rightarrow b=0$ Find $c$: $-1+0+c=0\\ \rightarrow c=1$ Hence, $a=-1\\b=0\\c=1$ Substitute back to the initial equation: $y=-x^2+1$
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