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

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

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

Answer 1

To find the high or low point of the parabola described by the quadratic equation \( y = -6x^2 + 3x + 8 \), we can determine the vertex of the parabola. Since the coefficient of \( x^2 \) is negative, the parabola opens downward, indicating that the vertex is a high point.

The x-coordinate of the vertex for a quadratic equation given by \( y = ax^2 + bx + c \) can be found using the formula:
\[
x = -\frac{b}{2a}
\]
In this equation:
- \( a = -6 \)
- \( b = 3 \)

Plugging in those values:
\[
x = -\frac{3}{2(-6)} = -\frac{3}{-12} = \frac{1}{4} = 0.25
\]

Now, we can find the corresponding \( y \)-value by substituting \( x = 0.25 \) back into the equation:
\[
y = -6(0.25)^2 + 3(0.25) + 8
\]
Calculating \( (0.25)^2 = 0.0625 \):
\[
y = -6(0.0625) + 0.75 + 8
\]
\[
y = -0.375 + 0.75 + 8 = 8.375
\]

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

Now, let's check the given statements:

1. \( (0.5, 9) \) is the high point on the parabola. (Incorrect)
2. \( (-1, -1) \) is the low point on the parabola. (Incorrect)
3. \( (0.25, 8.375) \) is the low point on the parabola. (Incorrect)
4. \( (0.25, 8.375) \) is the high point on the parabola. (Correct)

Thus, the correct response is:

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