find x-intercepts
y=(x-1)squared + 2
y= (x+1)squared -1
completing the square
2xsquare -4x +1 =0
3xsquare - 5x -2=0
thank you
$\displaystyle y=(x-1)^2 + 2$
$\displaystyle y=x^2 -2x +3$
$\displaystyle b^2 - 4ac = (-2)^2 - 4(1)(3) = 4-12 = -8 < 0$
The discriminant is less than 0 which means that it does not cross the x-axis hence you won't have x-intercepts.
Try the other equation yourself by checking the discriminant for the nature of the curve. If it's greater than or equal to zero then it will have x-intercepts. To find it, make y equal to 0 and solve for x.
$\displaystyle 2x^2 - 4x+1=0$
For quadratic equations in the form:
$\displaystyle ax^2+bx+c$
The general rule to completing the square is:
$\displaystyle a\left(x + \frac{b}{2a}\right)^2 - \frac{b^2}{4a} + c$
Use this rule to complete the square for your equations.