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 - Skill Practice - Page 313: 37


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Work Step by Step

The standard form of the equation is: $y=ax^2+bx+c$ Given three points: $(-2,-13)\\(2,3)\\(4,5)$ Substitute: $-13=a(-2)^2+b(-2)+c\\3=a(2)^2+b(2)+c\\5=a(4)^2+b(4)+c$ We have the system: $4a-2b+c=-13\\4a+2b+c=3\\16a+4b+c=5$ Add the second equation to the first equation: $8a+2c=-10\\ \rightarrow 4a+c=-5$ (1) Multiply the first equation by $2$ and add to the third equation: $24a+3c=-21\\ \rightarrow 8a+c=-7$ (2) Subtract equation (1) from equation (2): $4a=-2\\a=\frac{-1}{2}$ Substitute $a$: $4(\frac{-1}{2})+c=-5\\c=-3$ Find b: $-2+2b-3=3\\ \rightarrow b=4$ Hence, $a=\frac{-1}{2}\\b=4\\c=-3$ Substitute back to the initial equation: $y=\frac{-1}{2}x^2+4x-3$
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