Write (6x² - 13x + 6) in either form and find its vertex figure.

6x² - 13x + 6 = (2x - 3)(3x - 2); {(12x - 13)² - 25} / 24

At x = 13 / 12,

6(13 / 12)² - 13(13 / 12) + 6 = -25 / 24

{2(13 / 12) - 3}{3(13 / 12) - 2} = -25 / 24

[{12(13 / 12) - 13}² - 25] / 24 = -25 / 24

vertex figure as (13 / 12, -25 / 24)

Write (10x² - 29x + 10) in either form and find its vertex figure.

10x² - 29x + 10 = (2x - 5)(5x - 2); {(20x - 29)² - 441} / 40

At x = 29 / 20,

10(29 / 20)² - 29(29 / 20) + 10 = -441 / 40

{2(29 / 20) - 5}{5(29 / 20) - 2} = -441 / 40

[{20(29 / 20) - 29}² - 441] / 40 = -441 / 40

vertex figure as (29 / 20, -441 / 40)

Write (15x² - 34x + 15) in either form and find its vertex figure.

15x² - 34x + 15 = (3x - 5)(5x - 3); {(15x - 17)² - 64} / 15

At x = 17 / 15,

15(17 / 15)² - 34(17 / 15) + 15 = -64 / 15

{3(17 / 15) - 5}{5(17 / 15) - 3} = -64 / 15

[{15(17 / 15) - 17}² - 64] / 15 = -64 / 15

vertex figure as (17 / 15, -64 / 15)