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Chapter 11: Q.276 (page 1157)

In the following exercise a) write the equation in standard form b) use properties of standard form to plot the graph:x=4y2+8y

Short Answer

Expert verified

The equation can be given asx=4(y+1)2-4

The graph can be given as

Step by step solution

01

Given information

We are given a equationx=4y2+8y

02

Write the equation in standard form 

We get

x=4y2+8yx=4(y2+2y)x=4(y2+2y+1)-4x=4(y+1)2-4

on comparing with standard equation we getrole="math" localid="1645507741742" a=4,h=-4,k=1

03

 find the axis of symmetry and the vertex of parabola

The axis of symmetry can be given as y=k

we get,role="math" localid="1645507944970" y=-1

And the vertex can be given as role="math" localid="1645507953505" (h,k)=(-4,-1)

04

Find the x-intercept 

Put y=0we get,

role="math" localid="1645507351999" x=4(0-1)2-4x=0

05

Find the point symmetric to (0,0) across the axis of symmetry

The point can be given as (0,-2)

06

Find y-intercept

Put x=0

x=4y2+8y4y2+8y=0y2+2y=0y(y+2)=0y=0andy=-2

The coordinates are(0,0),(0,-2)

07

plot the graph

The graph can be given as

08

Conclusion

The equation can be given asx=(y+1)2-4

The graph can be given as

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