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 basic differentiating rules. 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 Im wondering about this. Hope someone can help to clarify my problems.

It is infinity because the slope is undefined. This means it is vertical.

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Hmm, but yeah, even if the slope of sqrt y is 'undefined' as the y graph cuts the x-axis, some graphs show x-shapes and some are flat shapes.

Wondering if there is a general rule to see aside from just plotting it out since some question dont give the equation but just give a pictorial graph and ask you to transform.

This is because graphs cannot represent infinity. It can be proved by using calculus (limits).

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The graphs you're refering to probably have a different equation to and therefore are completely irrelevant. You have been given the correct explanation.

And if you're given a graph and asked to transform it, just do appropriate transformations (translation, dilation, reflection, etc.)! The slope at the vertex of the transformed graph of will still be undefined (that is, the tangent is a vertical line).

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But for example, the graph when it just crosses the x-axis will result in a x-shape when it is also a stationary point at the same time.

I have absolutely no idea what you're trying to say here. The question you asked has been answered.

If you need more explanation, please post the exact equation of the graph your asking about and then clearly explain what you don't understand about it.

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