Question

In Problem, identify the graph of each equation without completing the squares.

$x^2+4x+y+3=0$

Short answer

An equation is a graph of a parabola.

Step-by-step solution

Step 1. Given information.

An equation is$x^2+4x+y+3=0$.

Step 2. Identify the graph.

Consider the equation: $x^2+4x+y+3=0$.

The equation $A{x}^2+C{y}^2+Dx+Ey+F=0$where $A$and $C$both cannot be zero,

(a) Defines a parabola if $AC=0$.

(b) Defines an ellipse (or a circle) if $AC>0$.

(c) Defines a hyperbola if $AC<0$.

Comparing the given equation with the equation $A{x}^2+C{y}^2+Dx+Ey+F=0$. We can see that $A=1$and localid="1646726173993" $C=0$So, we get width="51">AC=0.

So, the given equation is the equation of a parabola.