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Chapter 11: Q.182E (page 1135)

In the following exercises, graph each equation.

x=-y2-2y+3

Short Answer

Expert verified

Given equation for the conic will be a parabola.

Step by step solution

01

Step 1. Identify the conic

Since, only one variable yis squared, conic will be a parabola.

02

Step 2. Covert the equation into vertex form

x=-y2-2y+3

x=-(y2+2y+1)+1+3

x=-(y+1)2+4

03

Step 3. Find the vertex, line of symmetry, x and y intercepts of the parabola

Vertex form of the parabola is given by,

x=a(y-k)2+h

Here, vertex of the parabola 鈫�(h,k)

Line of symmetryrole="math" localid="1645558321060" 鈫�y=k

Compare the vertex form of the parabola with the given equation,

x=-(y+1)2+4

Since, ais negative, parabola will open to the left.

Vertex role="math" localid="1645558244069" 鈫�(4,-1)

Line of symmetry鈫�y=-1

For x-intercepts,

Put y=0

role="math" localid="1645558449400" x=-(0+1)2+4

x=3

For y-intercepts,

Put x=0

0=-(y+1)2+4

(y+1)2=4

role="math" localid="1645558770453" y+1=卤2y=-3,1

04

Step 4. Graph the equation

Graph of the equation will be,

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