Math, asked by mohammadaslam33066, 10 months ago

draw the graph of polynomial x² +2x-15 & find the zeros​

Answers

Answered by Swarup1998
14

Part 1.

Let, y = x² + 2x - 15

Now, y = x² + 2x - 15

or, y = (x + 1)² - 16

or, (x + 1)² = y + 16 ..... (1)

This is an equation of a parabola whose vertex is at (- 1, - 16) and its axis x = - 1 is parallel to the y-axis.

Putting y = 0 in (1), we get

(x + 1)² = 16

or, (x + 1)² - 4² = 0

or, (x + 5) (x - 3) = 0

i.e., x = - 5, 3

So the parabola (1) intersects the x-axis at (- 5, 0) and (3, 0)

To draw the graph:

• Take the vertex (- 1, - 16) on the graph paper

• Take (- 5, 0) and (3, 0) on the x-axis

• Join (- 1, -16) with (- 5, 0) and (3, 0) with curves

• Stretch the two lines a little on upper side

# Take a look at the attached picture.

Part 2.

Now, x² + 2x - 15

= x² + 5x - 3x - 15

= x (x + 5) - 3 (x + 5)

= (x + 5) (x - 3)

This is the required factorization.

Thus the required zeroes are (- 5) and 3

Attachments:
Answered by balaji5126
1

Answer:

Given -

y

=

x

2

2

x

15

It can be graphed by plotting the following points

vertex, y-intercept, and x-intercepts

Vertex

x

=

b

2

a

)

=

(

2

)

2

×

1

=

1

At

x

=

1

y

=

1

2

2

(

1

)

15

=

1

2

15

=

16

Vertex

(

1

,

16

)

Y-Intercept

At

x

=

0

y

=

0

2

2

(

0

)

15

=

15

Y-Intercept

(

0

,

15

)

Its x-intercepts are

At

y

=

0

x

2

2

x

15

=

0

x

2

5

x

+

3

x

15

=

0

x

(

x

5

)

+

3

(

x

5

)

=

0

(

x

+

3

)

(

x

5

)

=

0

x

=

3

x

=

5

The two x- intercepts are

(

3

,

0

)

(

5

,

0

)

Plot the points

(

1

,

16

)

;

(

0

,

15

)

;

(

3

,

0

)

(

5

,

0

)

You will get the curve

Look at the graph

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