Question

2. Given this table of values, complete the table for the quadratic equation 3x² - 6x + 9 to find the values of the high or low point of the parabola.
x y
-3 54
-2 33
-1
0
1
2 9

The high or low point of this parabola is (_,_).

Answer 1

To find the values of the high or low point of the parabola, we need to complete the table by substituting the given x-values into the quadratic equation 3x² - 6x + 9 and solving for the corresponding y-values.

For x = -1:
y = 3(-1)² - 6(-1) + 9
y = 3(1) + 6 + 9
y = 3 + 6 + 9
y = 18

For x = 0:
y = 3(0)² - 6(0) + 9
y = 3(0) + 0 + 9
y = 0 + 0 + 9
y = 9

Therefore, the completed table is as follows:
x y
-3 54
-2 33
-1 18
0 9
1
2 9

To find the high or low point of the parabola, we compare the y-values in the table. The maximum or minimum point of a quadratic equation corresponds to the vertex of the parabola. In this case, the y-values of the points (-1, 18) and (0, 9) are the same, indicating that the parabola opens upwards and the vertex lies between these two points.

Thus, the high or low point of this parabola is (x, y) = (-0.5, 8.5)