Question

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?

Answer 1

The given equation is a Parabola

Explanation:

Given -

`(y+4)=(x-2)^2`

Let us rewrite the equation in a know form

`y+4=x^2-4x+4`
`ycancel (+4)-x^2-4xcancel(-4)=0`

`-x^2-4x+y=0`

Let us have the coics section equation

`Ax^2+Cy^2+Dx+Ey+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.