Using the roots, write an equation in vertex form where h = 1 and k = -8.

The vertex is (h, k).

y = a ( x - h )² + k

y = a ( x - 1)² - 8

To find the value of “a,” use coordinates of any other point on the graph:
Note: x-values in red, y-values in green, and a-value in blue.

y-intercept is (0, -6)

-6 = a ( 0 - 1 )² - 8
-6 = a ( -1 )² - 8
-6 = a ( 1 ) - 8
-6 + 8 = a - 8 + 8
2 = a

Therefore, the particular equation for this graph is:

y = 2 (x – 1)² – 8
y = 2 (x² – 2x + 1) – 8
y = 2x² – 4x + 2 – 8

y = 2x² – 4x – 6

Both methods yield the same equation.