Question

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

Answer 1

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)`