Question

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

Answer 1

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)`

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By substitution

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

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

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

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