2. 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
-.75 2.375
-.5 5
-.25
0 8
.25 8.375
.5
.75
1 5
Which of the following is correct?
• (-1,-1) is the low point of the parabola
• (.5,9) is the high point on the parabola
• (.25,8.375) is the high point on the parabola
• (.25,8.375) is the low point on the parabola
To find the high or low point of the parabola, we need to look for the vertex of the quadratic equation. The x-coordinate of the vertex can be found using the formula: x = -b/2a.
Given that the quadratic equation is in the form y = -6x² + 3x + 8, we can see that a = -6 and b = 3. Plugging these values into the formula, we get:
x = -3/(2(-6)) = -3/(-12) = 1/4 = 0.25
Now, we need to find the corresponding y-coordinate by substituting the x-coordinate 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
So, the high or low point of the parabola is (.25, 8.375).
Therefore, the correct answer is: (.25, 8.375) is the high point on the parabola.
To find the high or low point of the parabola, we need to find the vertex of the quadratic equation. The x-coordinate of the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.
For the given equation y = -6x² + 3x + 8, a = -6 and b = 3.
x = -3/(2*(-6))
x = -3/(-12)
x = 1/4
Substituting x = 1/4 into the equation y = -6x² + 3x + 8, we can find the y-coordinate of the vertex.
y = -6(1/4)² + 3(1/4) + 8
y = -6(1/16) + 3/4 + 8
y = -3/8 + 3/4 + 8
y = -3/8 + 6/8 + 8
y = 5/8 + 8
y = 5/8 + 64/8
y = 69/8
So, the vertex is located at (1/4, 69/8) which is approximately (0.25, 8.625).
Therefore, the correct answer is: (.25,8.375) is the high point on the parabola.
To find the values of the high or low point of the parabola represented by the quadratic equation y = -6x² + 3x + 8, you need to find the vertex of the parabola. The vertex represents either the highest or lowest point of the parabola depending on whether the coefficient of the x² term is positive (upward-opening parabola) or negative (downward-opening parabola).
The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a is the coefficient of the x² term, and b is the coefficient of the x term.
In this case, the quadratic equation is y = -6x² + 3x + 8, so a = -6 and b = 3.
x = -3 / (2 * (-6))
x = -3 / (-12)
x = 1/4
Now, to find the y-coordinate of the vertex, substitute the x-coordinate back into the equation y = -6x² + 3x + 8.
y = -6(1/4)² + 3(1/4) + 8
y = -6(1/16) + 3/4 + 8
y = -6/16 + 3/4 + 8
y = -3/8 + 3/4 + 8
y = -3/8 + 6/8 + 8
y = 3/8 + 8
y = 3/8 + 64/8
y = 67/8
Therefore, the vertex of the parabola is (1/4, 67/8).
Now you can use the table of values provided to determine the correct statement about the high or low point of the parabola:
(-1,-1) is not the vertex (1/4, 67/8), so it cannot be the low point of the parabola.
(.5,9) is not the vertex (1/4, 67/8), so it cannot be the high point of the parabola.
(.25,8.375) is not the vertex (1/4, 67/8), so it cannot be the high or low point of the parabola.
Therefore, the correct statement is: none of the statements provided are correct. The vertex (1/4, 67/8) represents the high point of the parabola.