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

4x² - 16x + 15 = (2x - 3)(2x - 5); (2x - 4)² - 1

At x = 2,

4(2)² - 16(2) + 15 = -1

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

{2(2) - 4}² - 1 = -1

vertex figure as (2, -1)

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

6x² - 19x + 15 = (2x - 3)(3x - 5); {(12x - 19)² - 1} / 24

At x = 19 / 12,

6(19 / 12)² - 19(19 / 12) + 15 = -1 / 24

{2(19 / 12) - 3}{3(19 / 12) - 5} = -1 / 24

[{12(19 / 12) - 19}² - 1] / 24 = -1 / 24

vertex figure as (19 / 12, -1 / 24)

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

6x² - 25x + 25 = (2x - 5)(3x - 5); {(12x - 25)² - 25} / 24

At x = 25 / 12,

6(25 / 12)² - 25(25 / 12) + 25 = -25 / 24

{2(25 / 12) - 5}{3(25 / 12) - 5} = -25 / 24

[{12(25 / 12) - 25}² - 25] / 24 = -25 / 24

vertex figure as (25 / 12, -25 / 24)