Question

Given this table of values, complete the table for the quadratic equation y=3x2−6x+9
to find the values of the high or low point of the parabola.

x to y
−3 to 54
−2 to 33
−1
0
1
2 to 9

Answer 1

Compute y = 3x^2 − 6x + 9 for the missing x-values:

- x = −1: y = 3(1) − 6(−1) + 9 = 3 + 6 + 9 = 18
- x = 0: y = 3(0) − 6(0) + 9 = 9
- x = 1: y = 3(1) − 6(1) + 9 = 3 − 6 + 9 = 6

Completed table:
-3 → 54
-2 → 33
-1 → 18
0 → 9
1 → 6
2 → 9

Since a = 3 > 0, the parabola opens upward and has a minimum (low point) at the vertex. The vertex x = −b/(2a) = 1, giving the low point (1, 6).