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Chapter 11: Q.279 (page 1157)

In the following exercise a) write the equation in standard form b) use properties of standard form to plot the graph:x=-2y2+4y

Short Answer

Expert verified

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

The graph of the parabola can be given as

Step by step solution

01

Given information

We are given an equationx=-2y2+4y

02

Write the equation in standard form 

We have,

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

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

03

Find the axis of symmetry and vertex of parabola

The axis of symmetry can be given as y=k

we have y=1

And the vertex can be given asrole="math" localid="1645511144589" (k,h)=(2,1)

04

Find x-intercept

Put y=0

we get

x=0

05

Find y-intercept

Put x=0

we get

-2y2+4y=0y2-2y=0y(y-2)=0y=0ory=2

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

06

Plot the graph

The graph can be given as

07

Conclusion

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

The graph of the parabola can be given as

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