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What is f(x)?

I dont understand how to solve quadratic functions. I'm supposed to solve f(x)-x^2+2x-3 by completing the square  but whenever I try to search how to do these kind of problems, I never see a problem with f(x) !!! Please help me D: 

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3 Answers

I was also wondering if you had written this correctly? Just as John R. said; f(x) is the "function of x" which I frequently just say f(x)=y.

f(x) is a notation for a "function of x." Usually it is written as f(x)= "something", which is an expression with x as what we call the independent variable. Many times f(x) and y are the same thing. In solving a quadratic equation you are looking for the roots of the expression in the form of a^2 + bx + c. And the roots are defined as the values where this expression equal zero (on a graph, it's where the curve crosses the x-axis). So what you are looking for is the values of x that satisfy x^2 + 2x - 3 = 0. (I'm guessing your teacher means f(x) = x^2 + 2x - 3) To start focus on the portion of this expression x^2 + 2x. Now ask yourself if you can find a number that when added to this will allow you to write it as a quantity squared i.e (x + k)^2. So we want (x + k)^2 which is the same as x^2 + 2xk + k^2 = x^2 + 2x. It looks like k = 1. So if we go back to the original equation, x^2 + 2x - 3 = 0. If we add k^2, that is 1, to both sides we get x^2 + 2x + 1 - 3 = 1. Now make the simplification you just determined: (x + 1)^2 - 3 = 1. (You just completed the square). Rearranging: (x - 1)^2 = 4. Can you solve this from here? Be sure to check your answers (there are two of them) by substituting them, one at a time, back into the original equation. The next topic you are likely to study is the quadratic equation. It is based on this method.

Hey there, well for starters f(x) is basically like saying Y.. ( ex: y=x+2 so this would be like f(x)=x+2 ) therefore you might have written the problem incorrectly because f(x) should be equal to something, ex f(x)=x^2+2x-3 that would be your function.