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 y
−3
54
−2
33
−1

0
1
2 9

Answer 1

First, compute y = 3x^2 − 6x + 9 for each x:

x | y
-3 | 54
-2 | 33
-1 | 18
0 | 9
1 | 6
2 | 9

Since a = 3 > 0 the parabola opens upward. The vertex (minimum) is at x = −b/(2a) = 6/(6) = 1, with y = 3(1)^2 − 6(1) + 9 = 6. So the low point is (1, 6).