Find the x-intercepts of the parabola with vertex (6,27) and y-intercept (0,-81). write answer in form (x1, y1) (x2, y2). if necessary, round to the nearest hundredth.

The vertex form of the equation is:

y = a (x - h) ² + k

- 81 = a (0 - 6) ² + 27

- 81 = 36 a + 27

- 108 = 36 a

a = - 108 : 36

a = - 3

y = - 3 (x - 6) ² + 27

y = - 3 (x² - 12 x + 36) + 27

y = - 3 x² + 36 x - 108 + 27

y = - 3 x² + 36 x - 81

y = - 3 (x² - 12 x + 27)

x² - 12 x + 27 = 0

x² - 9 x - 3 x + 27 = 0

x (x - 9) - 3 (x - 9) = 0

(x - 9) (x - 3) = 0

x 1 = 3, x 2 = 9

Answer:

The x-intercepts are (3, 0) and (9, 0).