Find x intercepts of

Question

y=2(x+3)^2 -12?

Answer 1

y=2(x+3)^2 -12

To find x intercept substitute y = 0 in given equation.

2(x+3)^2 -12 = 0

2[x^2 + 6x + 9] -12 = 0

2[x^2 + 6x + 9 - 6] = 0

x^2 + 6x + 3 = 0

Compare it to quadratic form ax^2+bx+c = 0

a = 1, b = 6, c = 3.

x = [-b±√(b^2-4ac)] / 2a

x = [-6±√(6^2-4(1)(3))] / 2(1)

x = [-6±√(36 - 12)] / 2

x = [-6±√(24)] / 2

x = [-6±2√(6)] / 2

x = 2[-3±√(6)] / 2

x = [-3±√(6)]

The solution are x = -3+√(6) , -3-√(6)