Question

A bike trail is drawn on a coordinate system. Each end of the trail is an x-intercept. The height of the trail is modeled by the function h(x) = -0.1x^2 - 0.3x +2.8 , where x is the horizontal distance in kilometers. How many meters is the horizontal distance of the trail?

Answer 1

4metres

Explanation:

Given the height of the trail modeled by the function h(x) = -0.1x^2 - 0.3x +2.8 , where x is the horizontal distance in kilometers

The horizontal distance occurs at the x intercept i.e at h(x) = 0

Substitute

0 = -0.1x^2 - 0.3x +2.8 ,

Multiply through by -10

0 = x^2 + 3x - 28

x^2 + 3x - 28 = 0

Factorize

x^2 + 7x - 4x - 28 = 0

x(x+7) - 4 (x+7) = 0

(x-4)(x+7) = 0

x-4 = 0 and x+7 = 0

x = 4 and -7

Since the danced cannot be negative, hence the horizontal distance of the trail is 4m