Find the x-intercept of the parabola with vertex (4,-1) and y - intercept (0,15). write answer in (x1, y1) (x2, y2) form : D ... ?

Vertex form of the equation:

y = a (x - h) ² + k;

15 = a (0 - 4) ² - 1

15 = 16 a - 1

16 a = 16

a = 16 : 16

a = 1

After that we have to transform the equation to the standard form:

y = (x - 4) ² - 1

y = x² - 8 x + 16 - 1

y = x² - 8 x + 15

Finally we have to find the zeroes:

x² - 8 x + 15 = 0

x² - 5 x - 3 x + 15 = 0

x (x - 5) - 3 (x - 5) = 0

(x - 5) (x - 3) = 0

x = 3, x = 5

Answer:

(x 1, y 1); (x 2, y 2) = (3, 0); (5, 0)