Write (15x² - 16x + 4) in either form and find its vertex figure.

15x² - 16x + 4 = (3x - 2)(5x - 2); {(15x - 8)² - 4} / 15

At x = 8 / 15,

15(8 / 15)² - 16(8 / 15) + 4 = -4 / 15

{3(8 / 15) - 2}{5(8 / 15) - 2} = -4 / 15

[{15(8 / 15) - 8}² - 4] / 15 = -4 / 15

vertex figure as (8 / 15, -4 / 15)

Write (15x² - 19x + 6) in either form and find its vertex figure.

15x² - 19x + 6 = (3x - 2)(5x - 3); {(30x - 19)² - 1} / 60

At x = 19 / 30,

15(19 / 30)² - 19(19 / 30) + 6 = -1 / 60

{3(19 / 30) - 2}{5(19 / 30) - 3} = -1 / 60

[{30(19 / 30) - 19}² - 1] / 60 = -1 / 60

vertex figure as (19 / 30, -1 / 60)

Write (25x² - 25x + 6) in either form and find its vertex figure.

25x² - 25x + 6 = (5x - 2)(5x - 3); {(10x - 5)² - 1} / 4

At x = 1 / 2,

25(1 / 2)² - 25(1 / 2) + 6 = -1 / 4

{5(1 / 2) - 2}{5(1 / 2) - 3} = -1 / 4

[{10(1 / 2) - 5}² - 1] / 4 = -1 / 4

vertex figure as (1 / 2, -1 / 4)