Question

What is the vertex form of `x = (2y - 3)^2 -11`?

Answer 1

Vertex form: `x=4(y-3/2)^2+(-11)`
Note this is a parabola with a horizontal axis of symmetry.

Explanation:

Vertex form (for a parabola with horizontal axis of symmetry):
`color(white)("XXX")x=m(y-b)^2+a`
with vertex at `(a,b)`

Conversion of given equation: `x=(2y-3)^2-11` into vertex form:

`color(white)("XXX")x=((2)*(y-3/2))^2 - 11`

`color(white)("XXX")x=2^2*(y-3/2)^2-11`

`color(white)("XXX")x=4(y-3/2)^2+(-11)`
(which is the vertex form with vertex at `(-11,3/2)`).
graph{x=(2y-3)^2-11 [-11.11, 1.374, -0.83, 5.415]}