Problem: The vertex of the parabola y=x2−8x+cy=x^{2}-8 x+cy=x2−8x+c will be a point on the xxx-axis if the value of ccc is:
Answer Choices:
A. −16-16−16
B. −4-4−4
C. 444
D. 888
E. 161616 Solution:
y=x2−8x+C=x2−8x+16+C−16=(x−4)2+C−16y=x^{2}-8 x+C=x^{2}-8 x+16+C-16=(x-4)^{2}+C-16y=x2−8x+C=x2−8x+16+C−16=(x−4)2+C−16 (a parabola). For its vertex to be on the xxx-axis, its coordinates must be (4,0)(4,0)(4,0) so that CCC must have the value 161616 .