Answer
$a=\pm5$
Work Step by Step
$f(g(x))=f(2x+a)=3(2x+a)^2-7=3(4x^2+4ax+a^2)-7$
The fact that it crosses the y-axis at $68$ means that $f(g(0))=68$.
Hence here $3(4\cdot0^2+4a\cdot0+a^2)-7=68\\3a^2=75\\a^2=25\\a=\pm5$
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 6 - Section 6.1 - Composite Functions - 6.1 Assess Your Understanding - Page 409: 56
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