Question

Use the method completing the square to write each of the following functions in the form y=a(x-h)^2+k. then identify the turning point and whether it is maximum or minimum.

(a) y=3x^2-12x+17.
(b) y=-5x^2+40x-70

Answer 1

(a) y = 3(x^2 -4x) +17 = 3(x^2 -4x +4) +17 -3*4
y = 3(x -2)^2 +5
The turning point at (2, 5) is a minimum.

(b) y = -5(x^2 -8x) -70 = -5(x^2 -8x +16) -70 +80
y = -5(x -4)^2 +10
The turning point at (4, 10) is a maximum.