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

1 Answer
May 4, 2017

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:

enter image source here

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:
enter image source here

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