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Chapter 11: Q.277 (page 1157)

In the following exercise a) write the equation in standard form b) use properties of standard form to plot the graph:x=y2+4y+5

Short Answer

Expert verified

The equation in standard form can be given asx=(y+2)2+1

The graph of the equation can be given as

Step by step solution

01

Given information

We are given an equationx=y2+4y+5

02

Step 2:Write parabola in standard form

We havex=y2+4y+5x=y2+4y+4+1x=(y+2)2+1

On comparing with standard form we geta=1,k=-2,h=1

03

Find the axis of symmetry and vertex

To find the axis of symmetry we have y=k

we get, y=-2

The vertex can be given asrole="math" localid="1645509461688" (h,k)=(1,-2)

04

Find x-intercept

To find put y=0

We get,

x=5

The coordinate is(5,0)

05

Find y-intercept

To find y-intercept put x=0

y2+4y+5=0

The roots of the above equation are imaginary hence the equation does not have a y-intercept

06

Plot the graph

The graph can be given as

07

Conclusion

The equation can be given asx=(y+2)2+1

The graph can be given as

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