x Substituted Evaluate True Statement? 12 %C2%A0 %C2%A0 %C2%A0 24 %C2%A0 %C2%A0 %C2%A0 36 %C2%A0 %C2%A0 %C2%A0 48 %C2%A0 %C2%A0 %C2%A0 When set off, a certain firework follows the path of the quadratic function%C2%A0 h=−2536x2+1623x , where: h= %C2%A0the height of the firework in feet. x= %C2%A0the horizontal distance it travels in feet. To determine how far the firework will travel before reaching the ground, determine which value of x%C2%A0in table is a solution to the equation%C2%A0 0=−2536x2+1623x . (1 point) Responses 24 feet 24 feet 48 feet 48 feet 12 feet 12 feet 36 feet

To find out how far the firework will travel before reaching the ground, we need to determine the values of \( x \) when the height \( h = 0 \). This leads us to solve the equation:

\[
0 = -2536x^2 + 1623x
\]

We can factor this equation:

\[
0 = x(-2536x + 1623)
\]

This gives us two potential solutions:

1. \( x = 0 \) (the starting point)
2. \( -2536x + 1623 = 0 \)

To solve for \( x \) from the second equation:

\[
-2536x + 1623 = 0
\]

Rearranging gives:

\[
2536x = 1623
\]

Dividing both sides by 2536:

\[
x = \frac{1623}{2536}
\]

Calculating this value:

\[
x \approx 0.6401 \, \text{feet}
\]

Now, since we are looking for specific values provided in the table (12 feet, 24 feet, 36 feet, and 48 feet), we need to evaluate the quadratic function at these values to see which one (if any) results in \( h = 0 \).

Calculating \( h \) at each of these \( x \) values:

1. **For \( x = 12 \)**:

\[
h = -2536(12^2) + 1623(12)
\]
\[
h = -2536(144) + 1623(12)
\]
\[
h = -364224 + 19476
\]
\[
h = -344748 \, \text{(the firework is below ground)}
\]

2. **For \( x = 24 \)**:

\[
h = -2536(24^2) + 1623(24)
\]
\[
h = -2536(576) + 1623(24)
\]
\[
h = -1460160 + 38952
\]
\[
h = -1421208 \, \text{(the firework is below ground)}
\]

3. **For \( x = 36 \)**:

\[
h = -2536(36^2) + 1623(36)
\]
\[
h = -2536(1296) + 1623(36)
\]
\[
h = -3282176 + 58428
\]
\[
h = -3223748 \, \text{(the firework is below ground)}
\]

4. **For \( x = 48 \)**:

\[
h = -2536(48^2) + 1623(48)
\]
\[
h = -2536(2304) + 1623(48)
\]
\[
h = -5838976 + 77844
\]
\[
h = -5760132 \, \text{(the firework is below ground)}
\]

Since the only values we calculated are negative heights, it appears at all of these positions, the firework has not yet reached ground level.

Now let’s check the values again, as the first height calculation should have alerted us to the quadratic nature of the function. Given that the discriminant indicates real outputs at precise coordinates, only a specific provided value indicates a height of zero. The question asks which value is the solution, implying at trajectory level only.

However, to summarize, based on the provided table values, none of them produce \( h = 0 \). The firework reaches the ground at:

\[
x \approx 0.6401
\]

Given this factor, none of the current options are feasible. The closest conceptual answer is derived functionally as none tally to heights of zero visibly in output measurement. Thus select a range that sits accordingly based on phrased indication versus height calculated angels.