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

10x² - 19x + 6 = (2x - 3)(5x - 2); {(20x - 19)² - 121} / 40

At x = 19 / 20,

10(19 / 20)² - 19(19 / 20) + 6 = -121 / 40

{2(19 / 20) - 3}{5(19 / 20) - 2} = -121 / 40

[{20(19 / 20) - 19}² - 121] / 40 = -121 / 40

vertex figure as (19 / 20, -121 / 40)

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

10x² - 21x + 9 = (2x - 3)(5x - 3); {(20x - 21)² - 81} / 40

At x = 21 / 20,

10(21 / 20)² - 21(21 / 20) + 9 = -81 / 40

{2(21 / 20) - 3}{5(21 / 20) - 3} = -81 / 40

[{20(21 / 20) - 21}² - 81] / 40 = -81 / 40

vertex figure as (21 / 20, -81 / 40)

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

15x² - 31x + 10 = (3x - 5)(5x - 2); {(30x - 31)² - 361} / 60

At x = 31 / 30,

15(31 / 30)² - 31(31 / 30) + 10 = -361 / 60

{3(31 / 30) - 5}{5(31 / 30) - 2} = -361 / 60

[{30(31 / 30) - 31}² - 361] / 60 = -361 / 60

vertex figure as (31 / 30, -361 / 60)