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

(−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.
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.

Answer 1

To find the high or low point of the parabola represented by the quadratic equation \( y = -6x^2 + 3x + 8 \), we need to determine the vertex of the parabola. Since the leading coefficient (the coefficient of \( x^2 \)) is negative, this parabola opens downwards, meaning it has a maximum (high point).

The x-coordinate of the vertex can be found using the formula:
\[
x = -\frac{b}{2a}
\]
where \( a = -6 \) and \( b = 3 \):

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

Next, we can substitute \( x = 0.25 \) back into the equation to find the corresponding \( y \)-value:

\[
y = -6(0.25)^2 + 3(0.25) + 8
\]
Calculating \( (0.25)^2 \):
\[
= 0.0625
\]

Now substituting:
\[
y = -6(0.0625) + 3(0.25) + 8
\]
\[
= -0.375 + 0.75 + 8
\]
\[
= 8.375
\]

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

Now, let's look at your response options:
- (−1,−1) is the low point on the parabola.
- (0.25,8.375) is the low point on the parabola.
- (0.5,9) is the high point on the parabola.
- (0.25,8.375) is the high point on the parabola.

The correct answer based on our calculations is:
**(0.25, 8.375) is the high point on the parabola.**