Ask a New Question
Menu

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 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.

(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.
Skip to navigation

page 14 of 14

1 answer

To analyze the quadratic equation \( y = -6x^2 + 3x + 8 \), we need to calculate the values of \( y \) for the given \( x \) values in the table:

  1. Calculate \( y \) for \( x = -1 \): \[ y = -6(-1)^2 + 3(-1) + 8 = -6(1) - 3 + 8 = -6 - 3 + 8 = -1 \]

  2. Calculate \( y \) for \( x = -0.75 \): \[ y = -6(-0.75)^2 + 3(-0.75) + 8 = -6(0.5625) - 2.25 + 8 = -3.375 - 2.25 + 8 = 2.375 \]

  3. Calculate \( y \) for \( x = -0.5 \): \[ y = -6(-0.5)^2 + 3(-0.5) + 8 = -6(0.25) - 1.5 + 8 = -1.5 - 1.5 + 8 = 5 \]

  4. Calculate \( y \) for \( x = -0.25 \): \[ y = -6(-0.25)^2 + 3(-0.25) + 8 = -6(0.0625) - 0.75 + 8 = -0.375 - 0.75 + 8 = 6.875 \]

  5. Calculate \( y \) for \( x = 0.5 \): \[ y = -6(0.5)^2 + 3(0.5) + 8 = -6(0.25) + 1.5 + 8 = -1.5 + 1.5 + 8 = 8 \]

  6. Calculate \( y \) for \( x = 0.75 \): \[ y = -6(0.75)^2 + 3(0.75) + 8 = -6(0.5625) + 2.25 + 8 = -3.375 + 2.25 + 8 = 6.875 \]

  7. Calculate \( y \) for \( x = 1 \): \[ y = -6(1)^2 + 3(1) + 8 = -6 + 3 + 8 = 5 \]

Now, the completed values are:

x      |   y
---------------
−1     |  −1
−0.75  |  2.375
−0.5   |  5
−0.25  |  6.875
0      |  8
0.25   |  8.375
0.5    |  8
0.75   |  6.875
1      |  5

Now we need to find the vertex of the parabola, which indicates the high or low points. Given that the parabola opens downwards (as indicated by the negative coefficient of \( x^2 \)), the vertex will be the high point.

To find the x-coordinate of the vertex, we use the formula: \[ x = -\frac{b}{2a} = -\frac{3}{2(-6)} = \frac{3}{12} = 0.25 \]

Now substituting \( x = 0.25 \) back into the equation to find the y-coordinate: \[ y = -6(0.25)^2 + 3(0.25) + 8 = -6(0.0625) + 0.75 + 8 = -0.375 + 0.75 + 8 = 8.375 \]

Thus, the high point of the parabola is \( (0.25, 8.375) \).

Conclusion

The correct response is: (0.25, 8.375) is the high point on the parabola.