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 30 feet 30 feet 15 feet

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 30 feet 30 feet 15 feet

Answer 1

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

Factoring out an x from the equation, we get:
x(-x + 15) = 0

Setting each factor equal to zero and solving for x, we get:
x = 0 or -x + 15 = 0

Solving -x + 15 = 0, we get:
-x = -15
x = 15

So the firework will travel 15 feet before it reaches the ground.

Answer 2

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

Step 1: Set the equation equal to zero:
-x^2 + 15x = 0

Step 2: Factor out the common term:
x(-x + 15) = 0

Step 3: Use the zero-product property:
x = 0 or -x + 15 = 0

Step 4: Solve for x:
x = 0 or x = 15

The two solutions for x are 0 and 15, but we are interested in the distance the firework travels, so we discard the solution x = 0 because it represents the starting point.

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

Answer 3

To determine how far the firework will travel before it reaches the ground, Isla needs to solve the quadratic equation -x^2 + 15x = 0.

Step 1: Factor out an x from both terms:
x(-x + 15) = 0

Step 2: Set each factor equal to zero and solve for x:
x = 0 or -x + 15 = 0

For the first factor, x = 0 means the firework has not traveled horizontally and has not reached the ground yet.

For the second factor, we can solve for x:
-x + 15 = 0
x = 15

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