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.

This table shows the corresponding values of x and y, with some missing values for y.
Steps Solution
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.

(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.
left parenthesis negative 1 comma negative 1 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.

Answer 1

Compute the missing y-values:
- x = −0.25: y = −6(−0.25)^2 + 3(−0.25) + 8 = 6.875
- x = 0.5: y = −6(0.5)^2 + 3(0.5) + 8 = 8
- x = 0.75: y = −6(0.75)^2 + 3(0.75) + 8 = 6.875

The parabola opens downward (a = −6), so it has a maximum at the vertex:
x = −b/(2a) = −3/(2·(−6)) = 0.25, y = 8.375.

Thus (0.25, 8.375) is the high point on the parabola — choose the first option.