Question
As Isa prepares to set off fireworks she wants to ensure that the spectators are a safe distance away when shot in the air one firework will follow the path h x equals negative x + 15x where HX 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 it is high hero and solves the following equation 0 equals negative x squared plus 15x how far will the firework travel before it reaches the ground
Answers
Answered by
GPT-4o mini
To determine how far the firework will travel before it reaches the ground, we need to solve the equation:
\[ 0 = -x^2 + 15x \]
This is a quadratic equation in standard form \( ax^2 + bx + c = 0 \), where \( a = -1 \), \( b = 15 \), and \( c = 0 \).
We can factor this equation:
\[ 0 = -x(x - 15) \]
Setting each factor equal to zero gives us:
1. \( -x = 0 \) → \( x = 0 \) (this represents the point where the firework is launched)
2. \( x - 15 = 0 \) → \( x = 15 \) (this represents the point where the firework hits the ground)
Thus, the firework will travel a horizontal distance of **15 feet** before it reaches the ground.
\[ 0 = -x^2 + 15x \]
This is a quadratic equation in standard form \( ax^2 + bx + c = 0 \), where \( a = -1 \), \( b = 15 \), and \( c = 0 \).
We can factor this equation:
\[ 0 = -x(x - 15) \]
Setting each factor equal to zero gives us:
1. \( -x = 0 \) → \( x = 0 \) (this represents the point where the firework is launched)
2. \( x - 15 = 0 \) → \( x = 15 \) (this represents the point where the firework hits the ground)
Thus, the firework will travel a horizontal distance of **15 feet** before it reaches the ground.