Question

Given this table of values, complete the table for the quadratic equation y=3x^2−6x+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

Compute y = 3x^2 − 6x + 9 for each x:

x = −3: y = 54 (given)
x = −2: y = 33 (given)
x = −1: y = 3(1) −6(−1) +9 = 3 +6 +9 = 18
x = 0: y = 9
x = 1: y = 3 −6 +9 = 6
x = 2: y = 9 (given)

Completed table:

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

The parabola opens up (a = 3 > 0), so the vertex is a minimum. Writing y = 3(x−1)^2 + 6 shows the vertex (low point) is at (1, 6).