To identify the high or low point of the parabola represented by the quadratic equation \( y = -6x^2 + 3x + 8 \), we need to find the vertex of the parabola.
The vertex of a quadratic equation in standard form \( y = ax^2 + bx + c \) can be found using the formula: \[ x = -\frac{b}{2a} \] Here, \( a = -6 \) and \( b = 3 \). Plugging in the values, we have: \[ x = -\frac{3}{2 \cdot -6} = -\frac{3}{-12} = \frac{1}{4} = 0.25 \]
Now, we will substitute \( x = 0.25 \) back into the equation to find the corresponding \( y \)-value: \[ y = -6(0.25)^2 + 3(0.25) + 8 \] Calculating \( (0.25)^2 = 0.0625 \), we get: \[ y = -6(0.0625) + 3(0.25) + 8 \] \[ = -0.375 + 0.75 + 8 \] \[ = 0.375 + 8 \] \[ = 8.375 \]
Thus, the vertex of the parabola is \( (0.25, 8.375) \).
Since the coefficient \( a \) in this equation is negative (\( a = -6 \)), this means the parabola opens downward, which indicates that the vertex is a high point.
Now, given the provided options, the correct statement is:
- (0.25, 8.375) is the high point on the parabola.
Therefore, the answer to your question is:
- (0.25, 8.375) is the high point on the parabola.