# math help (1 Viewer)

#### cossine

##### Active Member
k = 1

you want to shift the curve 1 unit to the right. The graph P(x-k) is shifted k units to the right. So k = 1.

ii)
P(x) = (x+1)(x-2)^2

So just expand (x+1)(x-2)^2.

• Dashdorm24

#### CM_Tutor

##### Moderator
Moderator
Actually, there are two possible values of ...

• cossine

#### Dashdorm24

##### New Member
Actually, there are two possible values of ...
and what would that be ?

#### cossine

##### Active Member
and what would that be ?
I think he is referring case of k = -2 which I missed.

To shift a graph k units to the left the transformation is f(x+k) where k is positive.

• CM_Tutor

#### CM_Tutor

##### Moderator
Moderator
I think he is referring case of k = -2 which I missed.

To shift a graph k units to the left the transformation is f(x+k) where k is positive.
Yes, I am.

And @Dashdorm24, you can check each is valid by doing the transformation and seeing that the resulting has as a factor.

For example, taking (which is the same as , I'm just using as a dummy variable so that the transformation is clearer), and performing the transformation , as suggested by @cossine, gives:

and it has a single root at the origin and a double root at , just as would be expected from a shift of one unit to the right.

The second transformation, , which @cossine correctly identified from my hint, should produce a shift of 2 units to the left, moving the double root to the origin. Checking:

and it has a single root at and a double root at the origin, just as would be expected from a shift of two units to the left.

Noting that our given polynomial has , we can also predict that a shift downwards by 4 should give a transformed polynomial with a root at the origin. Check:

and it has a single root at and a double root at the origin, just as would be expected from a shift of four units to the down. (The point lies on the original polynomial, so a shift down of four should produce a root of the new polynomial at .)

These techniques can be combined, along with dilations, to produce other polynomials as required.