Question

hs of Quadratic Equations Quick Check
2 of 52 of 5 Items
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.

(0.5,9) 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 low point on the parabola.

Answer 1

To determine the high or low point of the parabola represented by the quadratic equation \(y = -6x^2 + 3x + 8\), we first need to find the vertex of the parabola. Since the coefficient of \(x^2\) is negative, the parabola opens downward, which means it will have a high point (the vertex).

The formula to find the x-coordinate of the vertex of a quadratic equation in the form \(y = ax^2 + bx + c\) is given by:

\[
x = -\frac{b}{2a}
\]

Here, \(a = -6\) and \(b = 3\). Plugging in these values:

\[
x = -\frac{3}{2(-6)} = \frac{3}{12} = 0.25
\]

Now, to find the corresponding y-coordinate, we substitute \(x = 0.25\) back into the equation:

\[
y = -6(0.25)^2 + 3(0.25) + 8
\]
\[
y = -6(0.0625) + 0.75 + 8
\]
\[
y = -0.375 + 0.75 + 8
\]
\[
y = 8.375
\]

The vertex, and therefore the high point, is at the coordinates \((0.25, 8.375)\).

Now, checking the provided options:

- **(0.25, 8.375) is the high point on the parabola.** - This is correct.
- **(−1, −1) is the low point on the parabola.** - Incorrect, as this point is not the lowest point.
- **(0.5, 9) is the high point on the parabola.** - Incorrect.
- **(0.25, 8.375) is the low point on the parabola.** - Incorrect.

So the correct response is:

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