To determine the vertex (high or low point) of the parabola described by the quadratic equation \( y = -6x^2 + 3x + 8 \), we first need to find the vertex of the parabola. The formula for the x-coordinate of the vertex of a quadratic function \( y = ax^2 + bx + c \) is given by:
\[ x = -\frac{b}{2a} \]
In this case, \( a = -6 \) and \( b = 3 \):
\[ x = -\frac{3}{2(-6)} = \frac{3}{12} = 0.25 \]
Next, we find the y-coordinate of the vertex by substituting \( x = 0.25 \) back into the equation:
\[ y = -6(0.25)^2 + 3(0.25) + 8 \] \[ y = -6(0.0625) + 0.75 + 8 \] \[ y = -0.375 + 0.75 + 8 \] \[ y = 8.375 \]
Thus, the vertex of the parabola is \( (0.25, 8.375) \).
Since the coefficient of \( x^2 \) (which is \( -6 \)) is negative, this indicates that the parabola opens downwards. Therefore, the vertex represents the high point of the parabola.
Given these calculations, the correct response is:
(0.25, 8.375) is the high point on the parabola.