# How do you identity if the equation y+4=(x-2)^2 is a parabola, circle, ellipse, or hyperbola and how do you graph it?

Feb 7, 2017

The given equation is a Parabola

#### Explanation:

Given -

$\left(y + 4\right) = {\left(x - 2\right)}^{2}$

Let us rewrite the equation in a know form

$y + 4 = {x}^{2} - 4 x + 4$
$y \cancel{+ 4} - {x}^{2} - 4 x \cancel{- 4} = 0$

$- {x}^{2} - 4 x + y = 0$

Let us have the coics section equation

$A {x}^{2} + C {y}^{2} + D x + E y + F = 0$

If the product of the coefficient of ${x}^{2}$ and ${y}^{2}$ is equal to zero, then the given equation is a Parabola.

In the given equation there is no ${y}^{2}$ term. The coefficient of ${y}^{2}$ is zero. Hence the product of the coefficients of ${x}^{2}$ and ${y}^{2}$ is equal to zero.

The given equation is a Parabola.