To determine how far the firework will travel before reaching the ground, we need to solve the equation:
\[ 0 = -2536x^2 + 1623x \]
This equation can be factored. Let's start by factoring out \(x\):
\[ 0 = x(-2536x + 1623) \]
Setting each factor equal to zero gives us two potential solutions:
- \(x = 0\) (which represents the initial position at launch).
- \(-2536x + 1623 = 0\)
Now, let's solve the second equation:
\[ -2536x + 1623 = 0 \ -2536x = -1623 \ x = \frac{1623}{2536} \]
Calculating the value of \(x\):
\[ x = \frac{1623}{2536} \approx 0.6404 \text{ feet} \]
Now that we have the potential horizontal distances where the firework reaches ground level, you can check the value of \(x\) from the table you mentioned. You’ll want to identify which value in the table coincides with \(0\) or approximately \(0.6404\).
If you provide the specific values from your table, I can help you determine which one is a solution corresponding to when the firework reaches the ground.