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
24 feet
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To determine which value of x in the table is a solution to the equation 0=−2536x2+1623x, we substitute each value of x into the equation and evaluate it. We are looking for the value of x that makes the equation equal to 0.
Substituting 12 into the equation:
0 = -2536(12)^2 + 1623(12)
0 = -2536(144) + 19476
0 = -365184 + 19476
0 = -345708
The equation is not true when x = 12, so 12 feet is not the correct answer.
Substituting 24 into the equation:
0 = -2536(24)^2 + 1623(24)
0 = -2536(576) + 19476
0 = -1479936 + 19476
0 = -1460452
The equation is not true when x = 24, so 24 feet is not the correct answer.
Substituting 36 into the equation:
0 = -2536(36)^2 + 1623(36)
0 = -2536(1296) + 19476
0 = -3316416 + 19476
0 = -3296940
The equation is not true when x = 36, so 36 feet is not the correct answer.
Substituting 48 into the equation:
0 = -2536(48)^2 + 1623(48)
0 = -2536(2304) + 19476
0 = -5937664 + 19476
0 = -5918188
The equation is not true when x = 48, so 48 feet is not the correct answer.
Therefore, none of the values in the table are solutions to the equation 0=−2536x2+1623x.