Given the table of values, complete the table for the quadratic equation y=−6x2+3x+8 to find the values of the high or low point of the parabola. x y −1 −1 −0.75 2.375 −0.5 5 −0.25 0 8 0.25 8.375 0.5 0.75 1 5 Which of the following is correct? (1 point) Responses (0.5,9) is the high point on the parabola. left parenthesis 0.5 comma 9 right parenthesis is the high point on the parabola. (0.25,8.375) is the high point on the parabola. left parenthesis 0.25 comma 8.375 right parenthesis is the high point on the parabola. (0.25,8.375) is the low point on the parabola. left parenthesis 0.25 comma 8.375 right parenthesis is the low point on the parabola. (−1,−1) is the low point on the parabola.

Answer 1

To determine the high or low point of the parabola defined by the quadratic equation \( y = -6x^2 + 3x + 8 \), we first recognize that this parabola opens downwards (since the coefficient of \( x^2 \) is negative), indicating that it has a high point (maximum), rather than a low point (minimum).

The high point (vertex) of a parabola in standard form \( y = ax^2 + bx + c \) can be found using the formula:

\[ x = -\frac{b}{2a} \]

In this case, \( a = -6 \) and \( b = 3 \):

\[ x = -\frac{3}{2 \times -6} = -\frac{3}{-12} = \frac{1}{4} = 0.25 \]

Next, we can find the corresponding \( y \) value by substituting \( x = 0.25 \) back into the equation:

\[ y = -6(0.25)^2 + 3(0.25) + 8 \] \[ = -6(0.0625) + 0.75 + 8 \] \[ = -0.375 + 0.75 + 8 \] \[ = 0.375 + 8 \] \[ = 8.375 \]

So, the vertex (the high point) of the parabola is at the point \( (0.25, 8.375) \).

Now, examining the provided options, the statement that matches our finding is:

(0.25, 8.375) is the high point on the parabola.

Thus, that would be the correct response.