Question

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

(0.25,8.375)
is the high point on the parabola.
left parenthesis 0.25 comma 8.375 right parenthesis is the high point on the parabola.

(−1,−1)
is the low point on the parabola.
left parenthesis negative 1 comma negative 1 right parenthesis is the low 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.

(0.5,9)
is the high point on the parabola.

Answer 1

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.**