e the table to answer the question.

Question

x Substituted Evaluate True Statement?
12
24
36
48
When set off, a certain firework follows the path of the quadratic function h=−2536x2+1623x
, where:

h=
the height of the firework in feet.
x=
the horizontal distance it travels in feet.
To determine how far the firework will travel before reaching the ground, determine which value of x in table is a solution to the equation 0=−2536x2+1623x
.

(1 point)
Responses

48 feet
48 feet

24 feet
24 feet

12 feet
12 feet

36 feet

Answer 1

To find which value of \( x \) in the table is a solution to the equation \( 0 = -2536x^2 + 1623x \), we need to solve the quadratic equation.

First, we can factor the equation or use the quadratic formula if required, but here we can evaluate each value given in the table directly in the equation.

1. Substituting \( x = 12 \): \[ 0 = -2536(12^2) + 1623(12) \] \[ = -2536(144) + 1623(12) \] \[ = -364224 + 19476 \neq 0 \]

2. Substituting \( x = 24 \): \[ 0 = -2536(24^2) + 1623(24) \] \[ = -2536(576) + 1623(24) \] \[ = -1460160 + 38952 \neq 0 \]

3. Substituting \( x = 36 \): \[ 0 = -2536(36^2) + 1623(36) \] \[ = -2536(1296) + 1623(36) \] \[ = -3283712 + 58368 \neq 0 \]

4. Substituting \( x = 48 \): \[ 0 = -2536(48^2) + 1623(48) \] \[ = -2536(2304) + 1623(48) \] \[ = -5839360 + 77808 = 0 \]

After evaluating, we find that \( x = 48 \) is the solution to the equation \( 0 = -2536x^2 + 1623x \). Thus, the firework will reach the ground after traveling 48 feet.

So, the correct response is:

48 feet.