To determine the high or low point of the parabola represented by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can first find the vertex of the parabola. The vertex occurs at \( x = -\frac{b}{2a} \) where \( a \) and \( b \) are the coefficients in the standard quadratic equation \( y = ax^2 + bx + c \).
Given:
- \( a = -6 \)
- \( b = 3 \)
We can calculate the x-coordinate of the vertex:
\[ x = -\frac{b}{2a} = -\frac{3}{2 \cdot -6} = -\frac{3}{-12} = \frac{1}{4} = 0.25 \]
Next, we substitute \( x = 0.25 \) into the quadratic equation to find the corresponding y-coordinate:
\[ y = -6(0.25)^2 + 3(0.25) + 8 \] \[ = -6(0.0625) + 0.75 + 8 \] \[ = -0.375 + 0.75 + 8 \] \[ = 8.375 \]
Thus, the vertex of the parabola is \( (0.25, 8.375) \).
Since the coefficient of \( x^2 \) is negative (\( a = -6 \)), the parabola opens downwards, indicating that the vertex represents the high point on the parabola.
So, the correct response is:
(0.25, 8.375) is the high point on the parabola.