Question

Question

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 , 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

7.5 feet
7.5 feet

−15 feet
negative 15 feet

15 feet
15 feet

30 feet
30 feet
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Answer 1

To determine how far the firework will travel before it reaches the ground, we need to solve the quadratic equation \(0 = -x^2 + 15x\).

Let's start by rearranging the equation:

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

We can factor out \(x\):

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

Now we can set each factor equal to zero:

1. \(x = 0\)
2. \(-x + 15 = 0\) which gives us \(x = 15\)

These roots indicate that the firework reaches the ground at \(x = 0\) feet (the launch point) and \(x = 15\) feet (the point of landing).

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

The correct response is:

15 feet.