Question

How do I convert Y= x^2 + 3x + 1 into vertex form?

Answer 1

y = (x +
`(3)/(2)` )² -
`(5)/(4)`

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

Given

y = x² + 3x + 1

add/ subtract ( half the coefficient of the x- term )² to x² + 3x

y = x² + 2(
`(3)/(2)` )x +
`(9)/(4)` -
`(9)/(4)` + 1

= (x +
`(3)/(2)` )² -
`(5)/(4)`