Understanding Y² Graphing and Confusing Points on the X-Axis

[qazxsw11111]

Hi everyone. I am familiar with the graphing of y² graph which is essentially sqrt of the graph then reflected in the x-axis.

However, I am confused at the points where the y= graph cuts the x-axis. According to differentiation, the gradient of the sqrt y graph should have a sqrt y at the denominator using quotient rule. If y=0, the gradient should be infinity. However, I do see some graphs with some other shapes (some crossing, some flat) at the x-axis so I am wondering about this.

Hope someone can help to clarify my problems.

 

[whs]

Have you tried simply plugging in points and making a rough graph?

 

[qazxsw11111]

Yeah of course that would work but I was wondering if there is a general rule to see aside from just plotting it out since some question don't give the equation but just give a pictorial graph and ask you to transform.

 

[Mark44]

Hi everyone. I am familiar with the graphing of y² graph which is essentially sqrt of the graph then reflected in the x-axis.

Can you be more specific about what you're trying to do? This doesn't make any sense to me. An ordinary graph of a function y = f(x) is a plot of the points (x, y) that satisfy the equation y = f(x). Are you trying to see what you get when you plot the pairs (x, y^2)?