SOLUTION: Find f(k - 1) when f(x) = 4x^2 - 3x + 4 Answer key provided, nothing I attempt so far step wise gets me to the correct answer however. Answer key says the answer is: "4k^2 -

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Question 1196940: Find f(k - 1) when f(x) = 4x^2 - 3x + 4
Answer key provided, nothing I attempt so far step wise gets me to the correct answer however.
Answer key says the answer is: "4k^2 - 11k + 11"
Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

f(x) = 4x^2 - 3x + 4
f(x) = 4(x)^2 - 3(x) + 4 ... highlight all the variables we're going to replace; note the use of parenthesis
f(k-1) = 4(k-1)^2 - 3(k-1) + 4 ... each x replaced with k-1
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.