Use the table to answer the 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
12 feet
12 feet
48 feet
48 feet
36 feet
36 feet
24 feet
To determine which value of x in the table is a solution to the equation 0=−2536x^2+1623x, we need to substitute each x value into the equation and evaluate if the equation is true or not.
For x = 12:
h = -2536(12)^2 + 1623(12) = -36672 + 19476 = -17196
Since the height is not zero, this is not a solution.
For x = 24:
h = -2536(24)^2 + 1623(24) = -174528 + 38952 = -135576
Since the height is not zero, this is not a solution.
For x = 36:
h = -2536(36)^2 + 1623(36) = -326592 + 58428 = -268164
Since the height is not zero, this is not a solution.
For x = 48:
h = -2536(48)^2 + 1623(48) = -3681792 + 77704 = -3604088
Since the height is not zero, this is not a solution.
None of the x values in the table is a solution to the equation 0=−2536x^2+1623x.