Question

What is the vertex form of `x= 4y^2 + 16y + 16`?

Answer 1

See a solution process below:

Explanation:

To convert a quadratic from `x = ay^2 + by + c` form to vertex form, `x = a(y - color(red)(h))^2+ color(blue)(k)`, you use the process of completing the square.

This equation is already a perfect square. We can factor out a `4` and complete the square:

`x = 4y^2 + 16y + 16 - color(red)(16)`

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

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

Or, in precise form:

`x = 4(y + (-2))^2 + 0`