Question 1196940
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f(x) = 4x^2 - 3x + 4
f(<font color=red>x</font>) = 4(<font color=red>x</font>)^2 - 3(<font color=red>x</font>) + 4 ... highlight all the variables we're going to replace; note the use of parenthesis
f(<font color=red>k-1</font>) = 4(<font color=red>k-1</font>)^2 - 3(<font color=red>k-1</font>) + 4 ... each <font color=red>x</font> replaced with <font color=red>k-1</font>
The use of color-coding is optional, but I find it helps to see the replacements much easier.


The task is to now expand and simplify
f(k-1) = 4(k-1)^2 - 3(k-1) + 4
f(k-1) = 4(k-1)(k-1) - 3(k-1) + 4
f(k-1) = 4(k^2-2k+1) - 3(k-1) + 4
f(k-1) = 4k^2-8k+4 - 3k+3 + 4
f(k-1) = 4k^2-11k+11



Side note:
Here's a common mistake I see many students doing
f(x) = 4x^2 - 3x + 4
f(k-1) = 4k-1^2 - 3k-1 + 4
This is NOT correct because we didn't involve parenthesis around the k-1 terms on the right hand side
The temptation may be to simply search-and-replace each x with k-1, but I would say it should be "replace x with (k-1)" to be more accurate.
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