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Chapter 10: Q 11. (page 677)

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

x2+4x+y+3=0

Short Answer

Expert verified

An equation is a graph of a parabola.

Step by step solution

01

Step 1. Given information.

An equation isx2+4x+y+3=0.

02

Step 2. Identify the graph.

Consider the equation: x2+4x+y+3=0.

The equation Ax2+Cy2+Dx+Ey+F=0where Aand Cboth 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 Ax2+Cy2+Dx+Ey+F=0. We can see that A=1and localid="1646726173993" C=0So, we get width="51">AC=0.

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

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