This seemingly simple math problem really has me stumped:

[math]y = f(x) = x^2-4x+3[/math]

[math]f(2) = ?[/math]

I tried to apply PEMDAS to solve this problem.

Well, PEMDAS says that

**goes after parens and exponents, right? And subtraction goes**

*multiplication***, right?**

*last*So I figured... Ok, I'll solve it in this order:

- Parens - nothing to do here
- Exponents - [imath]x^2 = 2^2 = 4[/imath]
- Multiplication - [imath]4x = 4 * 2 = 8[/imath]
- Division - nothing to do here
- Addition - [imath]8 + 3 = 11[/imath]
- Subtraction - [imath]4 - 11 = -7[/imath]

But no! Apparently there's some hidden rule I didn't know about, because the correct answer is actually [imath]-1[/imath].

It seems like this has something to do with [imath]-4x[/imath] being considered together as a negative number, rather than as a subtraction of [imath]4x[/imath] from [imath]x^2[/imath].

Can anyone please explain to me how this is the case?

And if so, how can we differentiate between a genuine subtraction operation vs. a negative number?

Is there a rule that can be consistently applied to an equation, to figure out whether we're subtracting [imath]4x[/imath] from [imath]x^2[/imath] or adding [imath]-4x[/imath] and [imath]x^2[/imath] together?

Many thanks in advance to anyone who can help.