I need to describe the graphing of x= (y+2)^2

Question

as well as find the intercepts,vertex,and start and end points

Answer 1

The graph of x = ay² is a parabola that opens either right or left as I say that it follows or runs like the x-axis (because you start with "x = ")

 

Since you have a '1' automatically in front of (y+2)², this means that you have a positive 'a' which means it opens to the right

 

As for the vertex....you can rewrite the equation to show the vertex translation....it will look like this:

(x - h) = (y - k)²   where (h,k) are the vertex coordinates.

so  

x = (y+2)² can be rewritten as (x - 0) = (y+2)² 

 

this means vertex shows up as (0, -2)......0 comes from (x-0) and the -2 comes from (y - -2) or (y+2)

 

As for the intercepts:  

Y-Intecept......you already have (0,-2) for the y-intercept.......to get this mathematically you can plug in 0 for 'x' which makes the equation    

  0 = (y+2)²  

if you square root both sides...you get 

0 = y + 2

then subtract 2 on both sides

-2 = y     so this gives you (0, -2)

X-Intecept......to get this mathematically you can plug in 0 for 'y' which makes the equation
x = (0+2)²  this makes

 

x = 2²

or

x=4........so this gives you (4, 0) for the x-intercept

 

 

 

 

Answer 2

I need to describe the graphing of x= (y+2)^2
as well as find the intercepts,vertex,and start and end points

 

x = (y+2)²

 

This is a horizontal or "sideways" parabola that opens either to the left or to the right, rather than a vertical parabola that opens up or down.  As written, the equation is in the "vertex form" for a quadratic:

 

x = a(y-h)² + k

 

Where (h,k) is the location of the vertex.  For your problem, a=1, h=-2, and k=0.  Hence the vertex lies at the point y=-2, x=0.  Since a is positive (a=1), the parabola opens to the right.  Had a been negative, it would open to the left.

 

Since the vertex lies on the y-axis, there is only one y-intercept and it is the vertex: y=-2, x=0.

 

The x-intercept is determined by setting y=0:

 

x = (0-2)² = 4

 

To graph it, plot the vertex and the x-intercept.  The axis of symmetry will be the line y=-2.  You may want to plug in a few other values for y to help you draw it as well.