Algebra 2 (1st Edition)

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

Chapter 4 Quadratic Functions and Factoring - 4.10 Write Quadratic Functions and Models - 4.10 Exercises - Quiz for Lessons 4.8-4.10 - Page 315: 12

Answer

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Work Step by Step

The standard form of the equation is: $y=ax^2+bx+c$ Given three points: $(-1,2)\\(4,-23)\\(2,-7)$ Substitute: $2=a(-1)^2+b(-1)+c\\-23=a(4)^2+b(4)+c\\-7=a(2)^2+b(2)+c$ We have the system: $a-b+c=2\\16a+4b+c=-23\\4a+2b+c=-7$ Subtract the first equation from the second equation: $15a+5b=-25\\ \rightarrow 3a+b=-5$ (1) Subtract the third equation from the second equation: $12a+2b=-6\\ \rightarrow 6a+b=-3$ (2) Substitute equation (1) from equation (2): $3a=-3\\ \rightarrow a=-1$ Substitute $a$ to equation (1): $3(-1)+b=-5\\ \rightarrow b=-2$ Find $c$: $-1-(-2)+c=2\\ \rightarrow c=1$ Hence, $a=-1\\b=-2\\c=1$ Substitute back to the initial equation: $y=-x^2-x+1$
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