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: 31


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Work Step by Step

The standard form of the equation is: $y=ax^2+bx+c$ Given three points: $(-4,-3)\\(0,-2)\\(1,7)$ Substitute: $-3=a(-4)^2+b(-4)+c\\-2=a(0)^2+b(0)+c\\7=a(1)^2+b(1)+c$ We have the system: $16a-4b+c=-3\\c=-2\\a+b+c=7$ Substitute $c$ into the equations, we have: $16a-4b=-1\\a+b= 9$ Multiply the second equation with $4$ and add to the first equation: $20a=35\rightarrow a=\frac{7}{4}$ Substitute $a$ into the second equation: $9-\frac{7}{4}=b\\ b=\frac{29}{4}$ Hence, $a=\frac{7}{4}\\b=\frac{29}{4}\\c=-2$ Substitute back to the initial equation: $y=\frac{4}{7}x^2+\frac{29}{4}x-2$
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