Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix C - Graphs of Second-Degree Equations - C Exercises: 24

Answer

parabola

Work Step by Step

Given: $y=x^{2}+2x$ By completing the square, we get $y+1=x^{2}+2x+1$ $y+1=(x+1)^{2}$ $y=(x+1)^{2}-1$ This is a parabola in the standard form as: $y=a(x-h)^{2}+k$ Here, $(h,k)=(-1,-1)$ which is the standard form of the equation of a parabola. The graph will be just like a graph of $y=x^{2}$ that is shifted 1 unit to the left and 1 unit downward.
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