HELP with Pre Cal problem

[MAIMOM]

My DD brought me this problem and says she is stumped and has no idea how they got the answer. Can anyone here help us?

 

Directions: Find the difference quotient and simplify your answer

 

f(x) = x squared -x +1,

 

f(2+h0 -f(2), {this line is over h}

 

h does not equal 0

 

:confused: stumped more than my DD

Edited September 27, 2012 by MAIMOM

[kiana]

note: x^2 means x squared.

 

f(2+h) means that you're putting (2+h) into the function instead of x. So wherever you see an x, change it to (2+h). So f(2+h) = (2+h)^2 - (2+h) + 1. We know that f(2) = 4-2+1 = 3, so our difference quotient is:

 

((2+h)^2 - (2+h) + 1) - 3

--------------------------

h

 

When we go to simplify this, we must be careful to square (2+h) properly. It is a *very* common mistake to try to write '4+h^2' instead ... watch out for this! (2+h)^2 = 2^2 + 2*2*h + h^2 = 4 + 4h + h^2. We also have to be careful to distribute the minus sign through the parentheses. So we get:

 

(4 + 4h + h^2 - 2 - h + 1) -3

----------------------------

h

 

After combining like terms, we get:

 

3h + h^2

---------

h

 

Another REALLY COMMON error to watch out for here is improper cancellation. We can't just start crossing off h's. We have to factor first. After factoring, we get:

 

h(3+h)

------

h

 

And then we can cancel the h's to get 3+h, which hopefully is the answer she was looking for; if not, there may be a typo in the answer book.

[MAIMOM]

note: x^2 means x squared.

 

f(2+h) means that you're putting (2+h) into the function instead of x. So wherever you see an x, change it to (2+h). So f(2+h) = (2+h)^2 - (2+h) + 1. We know that f(2) = 4-2+1 = 3, so our difference quotient is:

 

((2+h)^2 - (2+h) + 1) - 3

--------------------------

h

 

When we go to simplify this, we must be careful to square (2+h) properly. It is a *very* common mistake to try to write '4+h^2' instead ... watch out for this! (2+h)^2 = 2^2 + 2*2*h + h^2 = 4 + 4h + h^2. We also have to be careful to distribute the minus sign through the parentheses. So we get:

 

(4 + 4h + h^2 - 2 - h + 1) -3

----------------------------

h

 

After combining like terms, we get:

 

3h + h^2

---------

h

 

Another REALLY COMMON error to watch out for here is improper cancellation. We can't just start crossing off h's. We have to factor first. After factoring, we get:

 

h(3+h)

------

h

 

And then we can cancel the h's to get 3+h, which hopefully is the answer she was looking for; if not, there may be a typo in the answer book.

 

Thank you so much. I love this forum! HUGS Kiana for your help!:grouphug: