1. ## Polynomial function

The diagram below shows part of the graph of a polynomial function-
A possible equation for the rule of the function is:
The back of the book seems to think its y=(x-c)(b-x)^2 but i am pretty certain its y=(x+c)(x-b)^2. So am i wrong or is the book wrong?

2. Originally Posted by chaneliman
The diagram below shows part of the graph of a polynomial function-
A possible equation for the rule of the function is:
The back of the book seems to think its y=(x-c)(b-x)^2 but i am pretty certain its y=(x+c)(x-b)^2. So am i wrong or is the book wrong?
That depends how you define the value of c:

if c is a negative number then the book is correct

if you define c as absolute value of c then you are right. But I don't see any reason why you should do that

3. Hello, chaneliman!

Their graph is misleading, but the book is correct.

Consider the two intercepts anywhere on the x-axis.
Code:
      |
|                          *
|           *
|       *      *          *
|    *           *      *
- | -*- - - - - - - - -*- - - -
|* c                 b
|
*|
|

The general form would be: . $y \:=\x-c)(x-b)^2" alt="y \:=\x-c)(x-b)^2" />
. . no matter where the intercepts are.

If I were still teaching, I'd use this trick question on my students.
. . I'm just kidding . . . (Am I the only one laughing?)

4. i still don't understand this. y can't it be y=(x+c)(x-b)^2.

5. Originally Posted by chaneliman
The diagram below shows part of the graph of a polynomial function-
A possible equation for the rule of the function is:
The back of the book seems to think its y=(x-c)(b-x)^2 but i am pretty certain its y=(x+c)(x-b)^2. So am i wrong or is the book wrong?
Originally Posted by chaneliman
i still don't understand this. y can't it be y=(x+c)(x-b)^2.
First I'll point out that (x - b)^2 and (b - x)^2 are the same - you can expand and confirm this simple fact.

Now ...... look at the given graph. Clearly a reasonable value of c could be c = -3, say. A reasonable value of b could be b = 2, say.

You should have absolutely no problem in accepting that for these values of c and b, a possible rule for the graph is y = (x + 3)(x - 2)^2 = (x + 3)(2 - x)^2.

Sub c = -3 and b = 2 into y = (x-c)(b-x)^2 and you get the same equation.

BUT ...... Sub c = -3 and b = 2 into y = (x+c)(b-x)^2 and you DO NOT get the same equation ....
You get y = (x - 3)(2 - x)^2. This is clearly wrong. The x-intercept is at x = 3, NOT x = -3.

6. Originally Posted by chaneliman
i still don't understand this. y can't it be y=(x+c)(x-b)^2.
the general rule looks like that....

(x - a)(x - b)^2

because you must let what is inside the brackets equal to 0

so x - a = 0 then x = a .... thats the value you are looking for

e.g a = 5

x - 5 = 0

x = 5