What is the graph of the conic section defined by #x^2 + 4x - y + 9 = 0#?

1 Answer
Dec 9, 2016

Express #y# as a quadratic in #x# - #y# is a parabola

Explanation:

#x^2+4x-y+9=0#

Express #y# as a quadratic in #x#:
#y=x^2+4x+9#

Since the coefficient of #x^2# is #>0#, #y# has a minimum value

#y'=2x+4 -> y# has a minimum value at #x=-2# where #y=5#

The parabolic graph of #y# is shown below.

graph{x^2+4x+9 [-12.74, 12.59, -0.77, 11.9]}