Math, asked by isaacnewty, 1 year ago

draw the graph of the polynomial p(x)=x^2-6x+9 find its zeroes

Answers

Answered by sikku61
7

The first task here is to find the roots of the equation, that is where the graph intercepts the

x

axis. To do this, set

y

=

0

and then factorise:

x

2

+

6

x

+

9

=

0

(

x

+

3

)

2

=

0

x

=

3

In this case as

x

=

3

twice then the graph will "graze" x-axis at

x

=

3

, (intercept it only once). Note, if there were 2 distinct roots then the graph would cut straight the through the

x

axis at the 2 points and if there were no real roots then the graph would not intercept the

x

axis at all.

Find where the graph intercepts the

y

axis by setting

x

=

0

y

=

(

0

)

2

+

6

(

0

)

+

9

=

9

So our

y

intercept is at

(

0

,

9

)

We also have to find the turning point. This can be done in a number of ways, finding the midway point between the roots, setting the derivative equal to 0 or compete the square.

In this case we know that since

x

=

3

is the only root then that must also be the turning point.

As it is a quadratic where the

x

2

coefficient is positive then we know the graph will be a parabola with a minimum.

We now have all the information we need to graph the function. Simply mark on your points and sketch:

graph{x^2+6x+9 [-10, 10, -2, 10]}.Ans.

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