F(x) = aba
for the points (1, 2) and (2, ).

y

=

4

(

1

2

)

x

y

=

a

(

b

)

x

(

−

1

,

8

)

(

1

,

2

)

8

=

a

(

b

−

1

)

=

a

b

2

=

a

(

b

1

)

=

a

b

b

8

b

=

a

b

:

2

=

(

8

b

)

b

2

=

8

b

2

b

2

=

1

4

b

=

±

1

2

b

a

If

b

=

1

2

:

2

=

a

(

1

2

)

a

=

4

y

=

4

(

1

2

)

x

If

b

=

−

1

2

:

2

=

a

(

−

1

2

)

a

=

−

4y

=

4

(

1

2

)

x

y

=

a

(

b

)

x

(

−

1

,

8

)

(

1

,

2

)

8

=

a

(

b

−

1

)

=

a

b

2

=

a

(

b

1

)

=

a

b

b

8

b

=

a

b

:

2

=

(

8

b

)

b

2

=

8

b

2

b

2

=

1

4

b

=

±

1

2

b

a

If

b

=

1

2

:

2

=

a

(

1

2

)

a

=

4

y

=

4

(

1

2

)

x

If

b

=

−

1

2

:

2

=

a

(

−

1

2

)

a

=

−

4

Step-by-step explanation:

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

step-by-step explanation: