As Isla prepares to set off fireworks, when 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
To determine how far the firework will travel before it reaches the ground, we need to solve the quadratic equation -x^2 + 15x = 0.
We can solve this equation by factoring:
-x(x - 15) = 0
Setting each factor equal to zero:
x = 0
or
x - 15 = 0
Solving for x in the second equation:
x = 15
Therefore, the firework will travel 15 feet before it reaches the ground.
To determine the distance 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 the equation: x(-x + 15) = 0.
Step 3: Set each factor equal to zero and solve for x:
x = 0 or -x + 15 = 0.
To find the distances, we need to select the positive solution since distance cannot be negative.
Step 4: Solve for x:
-x + 15 = 0.
x = 15.
Therefore, the firework will travel 15 feet before it reaches the ground.
To determine how far the firework will travel before it reaches the ground, we need to solve the quadratic equation -x^2 + 15x = 0. Here's how you can do it:
Step 1: Write the equation in the general form: -x^2 + 15x = 0.
Step 2: Factor out common terms, if possible. In this case, you can factor out an x: x(-x + 15) = 0.
Step 3: Set each factor equal to zero and solve for x:
-x = 0 --> x = 0
-x + 15 = 0 --> x = 15
Step 4: Analyze the solutions:
Since x represents the horizontal distance, a value of x = 0 means the firework is launched from the starting point.
On the other hand, x = 15 indicates that the firework has traveled 15 feet horizontally.
Therefore, the firework will travel a distance of 15 feet before it reaches the ground.