Question

The stopping distance of a car traveling 25mph is 61.7ft, and for a car traveling 35mph it is 106ft. The stopping distance in feet can be described by the equation y=ax^2 + bx + c, where x is the speed in mph.

Find the values of a and b.

Answer 1

Well, you have two instances. Plug in the values and you'll have two equations in a and b. Solve them.

We know that when x is 0, y=0. (The car is not moving, so it has zero stopping distance.) So, c=0

61.7 = a(625)+b(25)
106 = a(1225)+b(35)

625a + 25b = 61.7
1225a + 35b = 106

multiply top by 7, bottom by 5, and subtract:

4375a + 175b = 431.9
6125a + 175b = 530

1750a = 98.1
a = 0.056
b = 1.067

Answer 2

import matplotlib.pyplot as plt
plt.plot([1,2,3,4])
plt.ylabel('some numbers')
plt.show()