x = y^2 and x = -4 y^2 - Math Central

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Question from Jil, a student:

My question is when dealing with parabolas, x=y^2, so that they are shifted on their side you could say,
what will happen to the graph if you change it to x=-4y^2. I understand that the - flips the graph in the other direction but can you simply just plug in numbers and increase the stretch of the y?

Hi Jil,

As you indicated the parabola x = y² is "on its side".

x = y^2

x = y²

You can determine the shape of x = -4 y² by substituting some numbers as you suggest. Sometimes you can see what happens without using specific points.

Suppose the curves are x = y² and x = -4 y² and and you want to find points on the two curves with the same y-value. Then substitute y² from the first equation into the second to obtain

x = -4 x

So to achieve the same y-value the x-value on the second curve must be (minus) 4 times the x-value on the first curve.

bothe curves

x = -4y² and x = y²

I hope this helps,
Penny

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