maximum vertical distance?

Question

Determine the maximum vertical distance, d, between the parabola,
y = −2x2 + 4x + 9
, and the line,
y = 5x + (−3)

 

Answer 1

HMMM.

 

The upside-down parabola passes through (1,11), its vertex, and y-intercept 9. As x increases without bound, y-values on the parabola grow more and more negative.

 

On the other hand, for the stated straight line, as x increases w/o bound, its y values increase steadily.

 

So it appears to me that the requested MAXIMUM VERTICAL DISTANCE between parabola & line is infinite.

Answer 2

the vertical distance is not limited - its maximum is infinity: check the problem...