SOLUTION: This is confusing. My teacher may have written the question wrong, but I want to make sure. If it is written correctly, I don't know how to do this. The function f is defined by

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: This is confusing. My teacher may have written the question wrong, but I want to make sure. If it is written correctly, I don't know how to do this. The function f is defined by      Log On


   

Question 962539: This is confusing. My teacher may have written the question wrong, but I want to make sure. If it is written correctly, I don't know how to do this.
The function f is defined by f(x)=x^2-2x-24. If f(x+3)=x^2+kx-21, what is the value of k?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Use the definition to find the result of x+3 as input of the function. Examine the format of the general form expressions to determine k.

Definition: f%28x%29=x%5E2-2x-24

Input (x+3): f%28x%2B3%29=%28x%2B3%29%5E2-2%28x%2B3%29-24
x%5E2%2B6x%2B9-2x-6-24
x%5E2%2B6x-2x%2B9-6-24
highlight_green%28f%28x%2B3%29=x%5E2%2B4x-21%29

You were given that highlight_green%28f%28x%2B3%29=x%5E2%2Bkx-21%29.
You can simply equate the two formulas for f(x+3).
x%5E2%2B4x-21=x%5E2%2Bkx-21
4x=kx
highlight%284=k%29