Question

Can you make a parabola with vertex in the second quadrant that will intersect with y=2x and y=x?

Answer 1

Any parabola of the forms:
`y=a(x-h)^2+k` where `a<0,h <0` and `k>0`

`x=a(y-k)^2+h` where `a>0,h<0` and `k>0`

Explanation:

First example:

Let `a = -1, h= -1`, and k = 1

`y=-(x--1)^2+1`

Here is a graph:

Please observe that the vertex is in the second quadrant and it intersects both lines (twice)

Second example is easier:

Let `a = 1, h = -1`, and `k =1`

`x = (y - 1)^2-1`

Here is a graph:

Please observe that the vertex is in the second quadrant and it intersects both lines (twice).