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. (0.25,8.375) 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.
The high or low point of a parabola (also known as the vertex) occurs when the x-coordinate is equal to -b/2a in the quadratic equation y = ax^2 + bx + c. In this case, a = -6 and b = 3.
To find the x-coordinate of the vertex, use the formula:
x = -b / (2a)
x = -3 / (2 * -6)
x = -3 / -12
x = 0.25
Substituting the x-coordinate into the equation, we find the y-coordinate of the vertex:
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
Therefore, the high point on the parabola is (0.25, 8.375).
Therefore, the correct answer is: (0.25, 8.375) is the high point on the parabola.
To find the high or low point of the parabola given by the equation y = -6x^2 + 3x + 8, we need to locate the vertex of the parabola. The vertex of a quadratic equation in the form y = ax^2 + bx + c is given by the formula x = -b/2a.
In this case, the equation is y = -6x^2 + 3x + 8, so the coefficient of x^2 is -6, the coefficient of x is 3, and the constant term is 8. Using the formula, we can find the x-coordinate of the vertex as:
x = -b/2a
x = -3/(2*(-6))
x = -3/(-12)
x = 1/4
Now, let's find the corresponding y-coordinate by substituting the x-coordinate back into the equation:
y = -6(1/4)^2 + 3(1/4) + 8
y = -6/16 + 3/4 + 8
y = -3/8 + 6/8 + 8
y = 11/8
Therefore, the high or low point of the parabola is (0.25, 1.375).
Among the given options, the correct answer is: (0.25, 8.375) is the high point on the parabola.
To find the high or low point of a parabola, we need to look for the vertex of the quadratic equation. The vertex form of a quadratic equation is given by:
y = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola.
In your case, the equation is given as y = -6x^2 + 3x + 8. Comparing it with the vertex form, we can see that a = -6, h = -b/2a, and k = c - ah^2.
First, let's find h (the x-coordinate of the vertex):
h = -b/2a = -3/(2*(-6)) = 0.25
Now, let's substitute this value of h into the equation to find k (the y-coordinate of the vertex):
k = c - ah^2 = 8 - (-6 * (0.25)^2) = 8 - 6 * 0.0625 = 8 - 0.375 = 7.625
Therefore, the vertex of the parabola is (0.25, 7.625).
Now, looking at the options provided:
(0.25, 8.375) is the high point on the parabola. This is not correct.
(−1,−1) is the low point on the parabola. This is not correct.
(0.25, 8.375) is the low point on the parabola. This is not correct.
(0.5, 9) is the high point on the parabola. This is not correct.
Hence, the correct answer is "(0.25, 7.625) is the high point on the parabola."