to iampebble:
like if i say y = (x+1)(x-3), the coefficient of x^2 is definitely
1
erm you mean (x)*(x) = x^2 postive? or did you take (1)*(x)? so
what you're trying to say that we shld look at these?
Hello hello, I hope you're online, anyway!
Let's say we expand (x+1)(x-3):
x^2 - 3x + x - 3
= x^2 - 2x -3
As I've mentioned, for a curve (which involves a
x^2), you can see from what I expanded
that the coefficient for x^2 is this case is 1, which is a
positive number. That's why I mentioned that without expansion, you
can see it is whether positive or negative because whether it is
positive or negative depends on the coefficients
of your x, because to get x^2, you use x*x, so if we have -x *
x, it will be -x^2, which means coefficient is -1, which is
negative. If we have -2x*x = -2x^2, which means coefficient is
-2, which is negative.
Simply put, if they give you a equation:
y = 2x^2 + 3x + 1
You can deduce that it is a smiling graph, why?
Because coefficient of x^2 is 2,which is
positive.
If they give you something not so straightforward:
y = (x+2)(x-3)
Yes, it will be troublesome to expand it out, and moreover it's
just sketching so it's even more unnecessary. But from that
equation, how do you end up with
"ax^2 + bx + c"? Bx + c is not of your
concern at all, because you're looking at a which
is infront of your x^2, and the ONLY way you
can get x^2 is only x * x, you can't get x^2 from x * 2, you
will get 2x, right? So you only have to look at the
COEFFICIENTS of the x's in your equation.
y = (x+2)(x-3)
is also
y = (1x+2)(1x-3)
1x * 1x = 1x^2
O.o I hope I'm not confusing you, seriously..