# How do you identity if the equation #y+x^2=-(8x+23)# is a parabola, circle, ellipse, or hyperbola and how do you graph it?

##### 1 Answer

This equation is a parabola. It opens down, and has a vertex of

#### Explanation:

- If you have both an
#x^2# and a#y^2# term, then you have either an**ellipse**or a**hyperbola**.

Move everything to one side. (The other side should be

#=0.# )

If both quadratic terms (

#x^2# and#y^2# ) have the same sign, then you have anellipse.

- If both terms have the same
coefficient, then you have a special kind of ellipse called acircle.If the quadratic terms have different signs, then you have a

hyperbola.

- If only one of your variables (
#x# or#y# ) is squared, then you have a**parabola**.

- If the
#x# is squared, you have a (classic) parabola that opens up/down.- If the
#y# is squared, you have a parabola that opens right/left.

- If neither
#x# or#y# have a squared term, you have a**line**.

========================================

In the equation

Factor the coefficient for *both*

Complete the square by adding

Move the 16 outside of the big brackets by *multiplying* it by the

A parabola in the form

- From the vertex, our next point is at "one unit right" and "
#1timesa# " units up. - From this point, go "one unit right" and "
#3timesa# " units up to find the next point. - Then, we go "one more unit right" and "
#5 times a # " units up to get another point. - Repeat the above steps, going left instead of right.

Note: here,

And that's it!