Write (6x² - 19x + 10) in either form and find its vertex figure.

6x² - 19x + 10 = (2x - 5)(3x - 2); {(12x - 19)² - 121} / 24

At x = 19 / 12,

6(19 / 12)² - 19(19 / 12) + 10 = -121 / 24

{2(19 / 12) - 5}{3(19 / 12) - 2} = -121 / 24

[{12(19 / 12) - 19}² - 121] / 24 = -121 / 24

vertex figure as (19 / 12, -121 / 24)

Write (9x² - 21x + 10) in either form and find its vertex figure.

9x² - 21x + 10 = (3x - 2)(3x - 5); {(6x - 7)² - 9} / 4

At x = 7 / 6,

9(7 / 6)² - 21(7 / 6) + 10 = -9 / 4

{3(7 / 6) - 2}{3(7 / 6) - 5} = -9 / 4

[{6(7 / 6) - 7}² - 9] / 4 = -9 / 4

vertex figure as (7 / 6, -9 / 4)

Write (10x² - 31x + 15) in either form and find its vertex figure.

10x² - 31x + 15 = (2x - 5)(5x - 3); {(20x - 31)² - 361} / 40

At x = 31 / 20,

10(31 / 20)² - 31(31 / 20) + 15 = -361 / 40

{2(31 / 20) - 5}{5(31 / 20) - 3} = -361 / 40

[{20(31 / 20) - 31}² - 361] / 40 = -361 / 40

vertex figure as (31 / 20, -361 / 40)