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: 32


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Work Step by Step

The standard form of the equation is: $y=ax^2+bx+c$ Given three points: $(-2,-4)\\(0,-10)\\(3,-7)$ Substitute: $-4=a(-2)^2+b(-2)+c\\-10=a(0)^2+b(0)+c\\-7=a(3)^2+b(3)+c$ We have the system: $4a-2b+c=-4\\c=-10\\9a+3b+c=-7$ Substitute $c$ into the equations. We have: $4a-2b=6\\9a+3b= 3$ Multiply the first equation with $3$ and the second equation with $2$: $12-6b=18\\18a+6b=6$ Add equations: $30a=24\rightarrow a=\frac{4}{5}$ Substitute $a$ into the first equation: $4\frac{4}{5}-2b=6\\ -2b=\frac{14}{5}\\ b=\frac{-7}{5}$ Hence, $a=\frac{4}{5}\\b=\frac{-7}{5}\\c=-10$ Substitute back to the initial equation: $y=\frac{4}{5}x^2-\frac{7}{5}x-10$
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