Answer:

Explanation:

Given:

x

2

+

3

x

−

10

=

0

.......................(1)

Determine

y

intercept

Read directly from equation (1)

y

intercept

=

−

10

'~~~~~~~~~~~~~ Tip! ~~~~~~~~~~~~~~~~~~~~

As the equation is already in the form

y

=

a

(

x

2

+

b

a

x

)

+

c

In this CASE

a

=

1

x

vertex

=

(

−

1

2

)

×

b

a

=

−

3

2

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Step 1

WRITE equation (1) as

(

x

2

+

3

x

)

−

10

=

0

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Step 2

ADD the adjustment constant

K

(

x

2

+

3

x

)

−

10

+

k

=

0

'~~~~~~~~~~~~~~~~~~~~~~~~~~~

Step 3

Move the power from

x

2

to outside the bracket

(

x

+

3

x

)

2

−

10

+

k

=

0

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Step 3

Remove the

x

from

3

x

(

x

+

3

)

2

−

10

+

k

=

0

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Step 4

Multiply the 3 inside the bracket by

1

2

(

x

+

3

2

)

2

−

10

+

k

=

0

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Step 4

If we multiply out the bracket we end up with an additional term to those in the original equation. That term is

(

3

2

)

2

derived from

(

?

+

3

2

)

(

?

+

3

2

)

=

(

3

2

)

2

. This term must be removed which is achieved by MAKING

k

=

−

(

3

2

)

2

So now we have

(

x

+

3

2

)

2

−

10

+

k

=

0

→

(

x

+

3

2

)

2

−

10

−

(

3

2

)

2

=

0

Completing the square

→

(

x

+

3

2

)

2

−

49

4

=

0

......................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Vertex

→

(

x

,

y

)

→

(

−

3

2

,

−

49

4

)

From equation (2)

(

x

+

3

2

)

2

=

49

4

Square rooting both sides

x

+

3

2

=

±

√

49

√

4

x

intercepts

=

−

3

2

±

7

2

=

-5 or +2)#

Tony B