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Chapter 11: Q.270 (page 1156)

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

y=-3x2-18x-29

Short Answer

Expert verified

The equation can be given asy=-3(x-3)2-2

The graph of parabola is

Step by step solution

01

Step : Given information

We are given a equation of parabolay=-3x2-18x-29

02

Write the equation in standard form  

We have,

y=-3x2-18x-29y=-3(x2-6x)-29y=-3(x2-6x+9)+27-29y=-3(x-3)2-2

comparing with standard form we get

a=-3,h=3,k=-2

03

Find the axis of symmetry and vertex of parabola

To find axis of symmetry put x=h

we get x=3

The vertex of the parabola can be given as(h,k)=(3,-2)

04

find y-intercept

To find y-intercept put x=0

we get,

role="math" localid="1645501855919" y=(0-3)2-2y=9-2y=7

The coordinate can be given as(0,7)

05

Find the point of symmetry to (0,7)across the axis of symmetry 

The point of symmetry can be given as(-6,-29)

06

Find the x-intercept

Put y=0

we get,

role="math" localid="1645502297666" -3(x-3)2-2=0(x-3)2=-23x-3=卤-23

the roots are imaginary

07

Plot the graph of the parabola

the graph can be given as

08

Conclusion

The equation in standard form can be given asy=-3(x-3)2-2

The graph of parabola can be given as

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