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?
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: . 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?)
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.
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
if the answer was -6
x - (- 6) = 0
x + 6 = 0
x = - 6
=] simple once you can understand it