To determine how far the firework will travel before it reaches the ground, we need to find the x-value when the height (h(x)) is equal to zero.
The equation is given as 0 = -x^2 + 15x.
To solve this quadratic equation, we can factor out an x:
0 = x(-x + 15)
Setting each factor to zero gives us:
x = 0 and -x + 15 = 0
Solving -x + 15 = 0 for x:
-x = -15
x = 15
Therefore, the firework will travel 15 feet before it reaches the ground. So the correct answer is 15 feet.
As Isla prepares to set off fireworks, she wants to ensure the spectators are a safe distance away. When shot in the air, one firework will follow the pathh(x)=−x^2+15x, where h(x) is the height of the firework, and x is the horizontal distance it travels in feet. To determine how far the firework will travel before it reaches the ground, Isla sets the height equal to zero, and solves the following quadratic equation: 0=−x^2+15x. How far will the firework travel before it reaches the ground?
-15 feet
7.5 feet
15 feet
30 feet
1 answer
1 answer