Question

When set off, a certain firework follows the path of the quadratic function h=−25/36 x2 + 16 2/3x, where:

h= the height of the firework in feet.
x= the horizontal distance it travels in feet.


To determine how far the firework will travel before reaching the ground, determine which value of x in table is a solution to the equation 0 = −25/36 x2 + 16 2/3x.

(1 point)

24 feet

12 feet

48 feet

36 feet

Answer 1

First convert 16 2/3 to a fraction: 16 2/3 = 50/3. The equation is

0 = −(25/36)x^2 + (50/3)x.

Multiply by 36: 0 = −25x^2 + 600x = x(−25x + 600).

So x = 0 or x = 600/25 = 24. The firework hits the ground at 24 feet.