m990540 wrote:
Bunuel, out of curiosity how would you graph (x^2) - 5x?
I understand how you did it here (
x2-4x-94661.html#p731476), but graphing it doesn't really seem to be working for this equation.
You don't really need the ability to draw the actual graph - You just need to know that an equation of this form with likely multiple roots would change signs at those roots.
Lets look at\(x^2-5x\)
This can be rewritten as \(x*(x-5)\), so points of interest are \(x = 0\) and \(x=5\) (where this function equals to zero). So, it can be deduced that this function will change a sign at \(x=0\) and then again at\(x=5\).
Whats the sign when\(x<0\). Lets put\(x=-1\) and see, it is +ve , so between 0 and 5, function will be negative and again for \(x > 5\), it will be positive.
So, without drawing exact graph, you can estimate that for x<0, the curve would be in 2nd quadrant (x is -ve and y is positive), between 0 and 5 it will be 4th quadrant (x is positive and y is negative) and again after x=5, it will be 1st quadrant (both x and y are positive)