Question

You can model that arch of a building entrance by using the equation y=−13(x−5)(x−6), where x and y are measured in feet. The x-axis represents the ground. Find the width of the arch at the ground.

Answer 1

1 unit

Explanation:

The arch has the shape of an inverted parabola.

It intersects the x-axis (the ground) at the roots of the equation

-13(x - 5)(x - 6) = 0

Since the equation is already factored, we solve the equation by setting x - 5 equal to zero and x - 6 equal to zero and solving the equations.

x - 5 = 0 or x 6 = 0

x = 5 or x = 6

The roots of the equation are x = 5 and x = 6.

The width is the distance between x = 5 and x = 6.

6 - 5 = 1

The width of the arch at the ground is 1 unit.