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Chapter 11: Q.266 (page 1156)

In the following exercises, graph each equation by using its properties:y=-6x2+12x+1

Short Answer

Expert verified

The graph of the parabola can be given as

Step by step solution

01

Step 1:  Given information

We are given a equationy=-6x2+12x+1

02

Check whether the parabola is upward or downward

As the coefficient of x2is negative hence the parabola is downward

03

Find the axis of symmetry 

we find the axis of symmetry by formula y=-b2a

Substituting the values we get

y=-12-12y=1

04

 Find the vertex of the parabola  

To find the vertex we substitute x=1in the equation we get,

y=-6x2+12x+1y=-6+12+1y=7

The vertex is at(1,7)

05

To find y-intercept put x=0

We get,

y=-6(0)2+12(0)+1y=1

The coordinate is (0,1)

As this coordinate is 1 units left to the axis of symmetry the other coordinate which is right to the axis of symmetry is(2,1)

06

Step 6; We write the x-intercept  

To find the x-intercept we put y=0

we get,

-6x2+12x+1=0

On using quadratic formula we get the roots as

x=-0.08and x=2.08

Therefore the coordinate is(-0.08,0),(2.08,0)

07

Plot the graph of the parabola

The graph can be given as

08

Conclusion

The graph of the parabola can be given as

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