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Chapter 11: Q.274 (page 1156)

In the following exercise graph each equation by using its properties:x=-y2+2y+4

Short Answer

Expert verified

The graph can be given as

Step by step solution

01

Given information

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

02

Check whether the parabola opens to right or left

As the coefficient of the square term is negative the parabola opens to the Left

03

Find the axis of symmetry

To find the axis of symmetry calculate

y=-b2ay=-2-2y=1

04

Find the vertex of parabola 

To find the vertex put y=1in the equation

we get,

x=-1+2+4x=5

The vertex of the parabola is (5,1)

05

Find y-intercept

To find x-intercept puty=0

we get

x=0+0+4x=4

The coordinate is(4,0)

06

Find y-intercept

Puty=0

we get,

x=0+0+4x=4

On solving using the quadratic formula we get x=3.236orx=-1.236

Hence the coordinates are

(0,3.236),(0,-1.236)

07

Plot the graph

The graph of parabola can be given as

08

Conclusion

The graph of the parabola is

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