What is the axis of symmetry and vertex for the graph #x-4 = 1/4 (y+1)^2#?

1 Answer
Jul 9, 2016

Vertex#->(x,y)=(4,-1)#

Axis of symmetry is #y=-1#

Explanation:

This is a quadratic in y. So instead of form#" "y=ax^"+bx+c# you have
#x=ay^2+by+c#

Consequently it is still of general shape #uu# but is rotated #90^0# clockwise to give #sub#

Write the equation as:#" "x=1/4(y+1)+4#

This equation format is in what is called 'Vertex Form'. With a slight adjustment you can read off the vertex coordinates directly from it

The #y# is inside the bracket of #x=1/4(y + color(red)(1))+color(blue)(4)# so

#y_("vertex")=(-1)xx color(red)(1) =-1#

#x_("vertex")=color(blue)(4)#
This is taken directly from the equation without change

So Vertex#->(x,y)=(4,-1)#

Tony B