To find the missing y-values for the parabola given by the equation \( y = -18x^2 + 34x + 78 \), we will substitute the given x-values into the equation.
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For \( x = 0 \): \[ y = -18(0)^2 + 34(0) + 78 = 78 \] So, the coordinates for \( x = 0 \) are \( (0, 78) \).
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For \( x = 11 \): \[ y = -18(11)^2 + 34(11) + 78 \] First, calculate \( 11^2 \): \[ 11^2 = 121 \] Now substitute: \[ y = -18(121) + 34(11) + 78 \] Calculate \( -18(121) \): \[ -18 \times 121 = -2178 \] Next, calculate \( 34(11) \): \[ 34 \times 11 = 374 \] Now substitute back into the equation: \[ y = -2178 + 374 + 78 \] Combine: \[ -2178 + 374 = -1804 \] Then, \[ -1804 + 78 = -1726 \]
So, the y-value for \( x = 11 \) is \( -1726 \).
Summary of Coordinates:
- For \( x = -1 \): \( y = 0 \)
- For \( x = 3 \): \( y = 2 \)
- For \( x = 0 \): \( y = 78 \)
- For \( x = 11 \): \( y = -1726 \)
The completed table: \[ \begin{array}{|c|c|} \hline \text{x-value} & \text{y-value} \ \hline -1 & 0 \ 3 & 2 \ 0 & 78 \ 11 & -1726 \ \hline \end{array} \]