graphing the vertex and axis of the symmetry

Question

I need help graphing the vertex and axis of the symmetry:
f(x)=(x+15)^2

Answer 1

y= (x+15)^2

 

general form is

 

(y-k)=(x-h)^2

 

comparing-----

 

h=-15

k=0

So, coordinates of the vertex are (-15,0)

Axis of symmetry----

 

X=-15

Answer 2

A parabola in the form 

 

y=(x-h)^2 + k

 

has a vertex at (h,k).  Notice that the x value of the vertex will be the opposite sign from the sign in the equation, but the y value will remain the same.  The axis of symmetry will always run straight up and down (vertically) through the vertex, and the equation for a vertical line in general is x=a.  We can use the x-value from our vertex for the a value in our equation for the axis of symmetry.

 

For example,

 

y = (x-3)^2 + 4       has a vertex at (3,4)  and an axis of symmetry equation of x=3

 

and    y = (x+3)^2 - 4       has a vertex at (-3,4)  and an axis of symmetry equation of x=-3.

 

Just be careful with your given equation because the k value is 0.  Or another way to write the equation would be 

 

y = (x+15)^2 + 0