Equation Parabola x^2-4x+2=2yx24x+2=2y?

1 Answer
Jun 26, 2018

Given: x^2-4x+2=2yx24x+2=2y

Divide both sides of the equation by 2:

y = 1/2x^2-2x+1y=12x22x+1

The above equation is now in the standard form y = ax^2+bx+cy=ax2+bx+c where a = 1/2a=12, b=-2b=2, and c = 1c=1; its roots can be found using the quadratic formula:

x = (-b+-sqrt(b^2-4(a)(c)))/(2a)x=b±b24(a)(c)2a

Substituting the values for, a, b, and c:

x = (-(-2)+-sqrt((-2)^2-4(1/2)(1)))/(2(1/2))x=(2)±(2)24(12)(1)2(12)

x = (2+-sqrt(4-2))/1x=2±421

x = 2+-sqrt2x=2±2

x = 2+sqrt2x=2+2 and x = 2-sqrt2x=22