Question

Rewrite the equation y^2 – 4y – 2x – 4 = 0 in standard form.

Answer 1

y² - 4y - 2x - 4 = 0

           +2x +4   +2x + 4

y² - 4y              = 2x + 4

            +4                 +4      

 (y - 2)²          = 2x + 8

             -8              -8

 (y - 2)²  - 8   = 2x

$\frac{(y - 2)^{2}}{2} - \frac{8}{2} = \frac{2x}{2}$

$\frac{1}{2}$(y - 2)² - 4 = x

x = $\frac{1}{2}$(y - 2)² - 4

Note: this is a parabola whose axis of symmetry is y = 2 and vertex is (-4, 2)