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 path h(x)=−x2+15x

Question

, 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=−x2+15x
. How far will the firework travel before it reaches the ground?(1 point)
Responses

30 feet
30 feet

−15
feet
negative 15 feet

7.5 feet
7.5 feet

15 feet

Answer 1

To determine how far the firework will travel before it reaches the ground, we need to solve the equation \( h(x) = 0 \):

\[ 0 = -x^2 + 15x \]

We can rearrange this equation:

\[ x^2 - 15x = 0 \]

Now, we can factor out an \( x \):

\[ x(x - 15) = 0 \]

Setting each factor equal to zero gives us:

1. \( x = 0 \)
2. \( x - 15 = 0 \) which simplifies to \( x = 15 \)

Thus, the firework will hit the ground when \( x = 0 \) (the starting point) and \( x = 15 \) feet.

Therefore, the firework will travel 15 feet before it reaches the ground.

Final answer: 15 feet