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Chapter 11: Q.269 (page 1069)

In the following exercise a) write the equation in standard form b) use properties of standard form to graph the parabola:

y=2x2-4x-2

Short Answer

Expert verified

The equation in standard form can be given asy=2(x-1)2-4

The graph of the parabola is

Step by step solution

01

Given information

We are given an equationy=2x2-4x-2

02

Write the equation in standard form 

We have,

y=2x2-4x-2y=2(x2-2x)-2y=2(x2-2x+1)-4y=2(x-1)2-4

Comparing with standard form we get a=2, h=1,k=-4

03

Find the axis of symmetry and vertex of parabola 

To find the axis of symmetry we use x=h

we get x=1

The vertex of parabola can be given as(h,k)=(1,-4)

04

Find y-intercept

To find y-intercept put x=0

we get,

role="math" localid="1645500719954" y=2(x-1)2-4y=2(-1)2-4y=2-4y=-2

05

Find the point of symmetry to (0,-2) across the axis of symmetry

The point of symmetry can be given as(2,-2)

06

Find the x-intercept

To find x-intercept put y=0

We get,

localid="1667921246558" 2(x-1)2-4=0(x-1)2=2x-1=卤2x=1卤2

Hence the coordinates are(1+2,0),(1-2,0)

07

Plot the graph of the parabola

The graph can be given as

08

Conclusion

The equation in standard form can be given asy=2(x-1)2-4

The graph can be given as

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