Question

The standard form of the equation of a parabola is `x=y^2-4y+20`. What is the vertex form of the equation?

Answer 1

Solution

Explanation:

The standard forms of the equation of the parabola are of `y^2=4ax` and `x^2=4ay` .

Here we have
`y^2-4y+16=x`

This is a shifted parabola of `y^2=4ax` form.

Make the `LHS` to the whole square part

Then,

`y^2-4y+4+12 =x`
`(y-2)^2=x-12`
Compare it with `RHS`

So we have
`(y-2)^2=4*1/4*(x-12)`

This is the standard form of the equation.