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

1 Answer
Mar 6, 2016

Vertex#->(x,y)->(-6,-4)#

Axis of symmetry#->y=-4#

Explanation:

Given: #" "x=1/4 y^2+2x-2#

#color(brown)("This is just like the normal quadratic but as if it is ")##color(brown)("rotated clockwise by "90^o)#

So let us treat it the same way!

Write as:#" "x=1/4(y^2+8y)-2#

#color(blue)("Axis if symmetry is at "y=(-1/2)xx(8) =-4)#

Also #color(blue)(y_("vertex")=-4)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
By substitution

#x_("vertex") =1/4(-4)^2+2(-4)-2#

#x_("vertex") =4-8-2#

#color(blue)(x_("vertex") =-6#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Tony B