Math problem in my textbook

Question

Determine the equation of the parabola with x-intercepts

1-√2 and 1+√2, and that passes through (2,4)

Answer 1

X-intercepts are 1±√2

x = 1±√2

x - 1 = ±√2

(x - 1)² = 2

(x - 1)² - 2 = 0

x² -2x +1 -2 = 0

x² -2x -1 = 0

The equation of parabola is:

y = a(x² -2x -1) where a is constant.

At (2, 4), solve for a.

4 = a(2² - 2(2) - 1)

4 = -a

a = -4

∴ y = -4(x² -2x -1) or

y = -4x² + 8x + 4