What does this mean? (parabola)

Question

The question is:

If ($x,y$) represents a point on the graph of $y = 2x + 1$, which of the following could be a portion of the graph of the set of points ($x,y^2$)?

The graphs are hard to put on and it is the general shape, not the specific graph that I am confused about.

To me I thought the question meant substituting ($x,y^2$) into $y = 2x + 1$. So in the end this gives you a root function.

But the answer said that the set of points ($x,y^2$) makes the equation $y = (2x+1)^2$. Could someone tell me where I went wrong or is this just ambiguous?

Thanks!

Answer 1

• "If (x,y) represents a point on the graph of y = 2x + 1" means you get a point whose coordinates are $$(x,2x+1)$$
• "which of the following could be a portion of the graph of the set of points $(x,y^2)$" is equal to "which of the following could be a portion of the graph of the set of points $(x,(2x+1)^2 = 4x^2 + 4x+1)$"

Hence you get the equation $$y = (2x+1)^2 = 4x^2 + 4x+1$$

Answer 2

As much as I can make out of this, your book has the right idea and just that the way the solution has been written is a bit confusing.

Better you go on as I am writing down:

1. Consider $y^2=z$
2. So the given equation becomes $z=(2x+1)^2=4x^2+4x+1$.

This is exactly what your book tried to convey. The set of points lies on a parabola.

If you keep the square root in that place, then you have $\sqrt{z}=2x+1$. And this is what you call a half of the previous parabola containing points where $z>0$, considering the positive square root only.

Hope this approach helps.