given the table of values, complete table for the quadratic equation
y=-6x^2+3x+8 to find the values of the high or low point of the parabola.
To find the high or low point of the parabola, we need to determine the vertex. The vertex of a quadratic equation in the form y = ax^2 + bx + c can be found using the formula x = -b / (2a).
In this case, the equation is y = -6x^2 + 3x + 8. So, a = -6, b = 3, and c = 8.
To find the x-coordinate of the vertex, we substitute these values into the formula:
x = -b / (2a) = -3 / (2*(-6)) = -3 / (-12) = 1 / 4
Now we find the y-coordinate of the vertex by substituting this x-coordinate back into the equation:
y = -6(1 / 4)^2 + 3(1 / 4) + 8
y = -6(1 / 16) + 3 / 4 + 8
y = -6 / 16 + 12 / 16 + 8
y = (-6 + 12 + 8) / 16
y = 14 / 16
y = 7 / 8
So, the high or low point of the parabola is (1 / 4, 7 / 8).
To complete the table, we substitute different values of x into the equation and calculate the corresponding y-values.
x | y
-------
-1 | 17
0 | 8
1/4 | 7/8 (high or low point of the parabola)
1 | 5
2 | -2
So, the completed table for the quadratic equation y = -6x^2 + 3x + 8 is:
x | y
--------
-1 | 17
0 | 8
1/4 | 7/8 (high or low point of the parabola)
1 | 5
2 | -2