SOLUTION: when plotting y=x^2-4x+3 i first found the values for when x is 0 and when y is 0, but how do you determine if its above the x axis and if its a maximum or a minimum? Thanks Mark

Question 133422: when plotting y=x^2-4x+3 i first found the values for when x is 0 and when y is 0, but how do you determine if its above the x axis and if its a maximum or a minimum?
Thanks
Mark
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
You can tell whether a parabola opens 'up' or 'down' by the sign on the high order term. In this case that term is . Since the sign is positive, the parabola opens 'up'.
To determine if the entire parabola lies above the x axis, you can set y = 0 and then solve for x. If there is no value of x that allows a y =0, then the entire parabola is above the x axis. If there is a single value of x that makes y=0, then the parabola "just touches" the x axis. If there are 2 values that make y=0, then the parabola crosses the x axis and has at least some part of below the x axis.
That is the case here:

Setting y =0 and solving for x yields values of x at 1 and 3 that allow y to be 0. --> two x values imply some part is below

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