Question

The standard form of the equation of a parabola is x = y2 - 4y + 20.

What is the vertex form of the equation?

A. x = (y - 4)2 + 4
B. x = (y - 2)2 + 16
C. x = (y - 2)2 + 4
D. x = (y - 4)2 + 12

Answer 1

The correct option is B.

Explanation:

The given equation is

`x=y^2-4y+20`

It can be written as

`x=(y^2-4y)+20`

Add and subtract
`(-(b)/(2a))^2` in the parenthesis.

`(-(b)/(2a))^2=((-4)/(2(1)))^2=(-2)^2=4`

Add and subtract 4 in the parentheses.

`x=(y^2-4y+4-4)+20`

`x=(y^2-4y+4)-4+20`

`x=(y+2)^2+16`

Therefore option B is correct.

Answer 2

If you would like to find the vertex form of the equation, you can calculate this using the following steps:

x = y^2 - 4 * y + 20
x = (y - 2)^2 - 4 + 20
x = (y - 2)^2 + 16

The correct result would be B. x = (y - 2)^2 + 16.