How do I find the speed in miles per hour when the stopping distance is 300 feet and the function is f(x)=.125x^2+2.3x+26.875

Question

We are working with quadratic regressions.  I found the function, but I can't figure out the speed when the stopping distance is 300 feet.  I believe the answer is 38.5, or when rounded 39 mph.

Answer 1

I assume f(x) is the stopping distance and x is the speed?  Then:

 

300 = (0.125)x² + (2.3)x + (26.875)

 0 = (0.125)x² +(2.3)x - (273.125)           [Subtracted 300 from both sides]

 

Use the quadratic formula to find x:

 

x = (-b/2a) ± (1/2a)√(b²-4ac)

 

Where a=(0.125), b=(2.3), and c=(-273.125).  You will get two answers, one positive and one negative.  The positive answer is the one you want.