Question

What is the maximum vertical distance between the line
y = x + 72
and the parabola
y = x2 for −8 ≤ x ≤ 9?What is the maximum vertical distance between the line
y = x + 72
and the parabola
y = x^2 for −8 ≤ x ≤ 9?

Answer 1

distance definition:
\[d =\sqrt{(x1-x2
)^{2}+(y1-y2)^{2}}\]
\[y1=x+72\]
\[y2=x^{2}\]
\[d=x+72-x^{2}\]
\[d(-8)=0\]
\[d(-9)=18\]
Maximum distance in [-8,-9] is 18
Attached is a graph