To complete the table for the parabola given by the equation \( y = -18x^2 + 34x + 78 \), we need to calculate the \( y \)-values for each provided \( x \)-value.
- For \( x = -1 \):
\[ y = -18(-1)^2 + 34(-1) + 78 \] \[ y = -18(1) - 34 + 78 \] \[ y = -18 - 34 + 78 = 26 \]
So, the coordinates are \((-1, 26)\).
- For \( x = 0 \):
\[ y = -18(0)^2 + 34(0) + 78 \] \[ y = 0 + 0 + 78 = 78 \]
So, the coordinates are \((0, 78)\).
- For \( x = 3 \):
\[ y = -18(3)^2 + 34(3) + 78 \] \[ y = -18(9) + 102 + 78 \] \[ y = -162 + 102 + 78 = 18 \]
So, the coordinates are \((3, 18)\).
- For \( x = 11 \):
\[ y = -18(11)^2 + 34(11) + 78 \] \[ y = -18(121) + 374 + 78 \] \[ y = -2178 + 374 + 78 = -1726 \]
So, the coordinates are \((11, -1726)\).
Now, filling out the table:
\[ \begin{array}{|c|c|} \hline \text{x-value} & \text{y-value} \ \hline -1 & 26 \ 0 & 78 \ 3 & 18 \ 11 & -1726 \ \hline \end{array} \]
Thus, the filled table looks like this:
- \(x = -1\), \(y = 26\)
- \(x = 0\), \(y = 78\)
- \(x = 3\), \(y = 18\)
- \(x = 11\), \(y = -1726\)
If there are any additional missing values or specific points you need, let me know!