College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 4 - Section 4.3 - Quadratic Functions and Their Properties - 4.3 Assess Your Understanding: 19

Answer

Option (H)

Work Step by Step

Note that: $x^2-2x = x^2-2x+(1-1) \\x^2-2x=(x^2-2x+1)-1 \\x^2-2x=(x-1)^2-1$ Thus, the given function can be written as: $f(x) =(x-1)^2-1$ RECALL: (1) The vertex form of a quadratic function whose vertex is at $(h, k)$ is: $f(x) = a(x-h)^2+k$ (2) The graph of the quadratic function $ax^2+bx+c$ is a parabola that opens: (i) upward when $a \gt 0$; (ii) downward when $a\lt 0$. Using the vertex form in (1) above, the given function has its vertex at $(1,-1)$. Using the rule in (2) above, with $a=1$, the given function's graph is a parabola that opens upward. The parabola that opens upward and whose vertex is at $(1, -1)$ is the one in Option (H).
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.