Question

Y= x^2 + 2x + 7 in vertex form

Answer 1

y = (x + 1)² + 6

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 + 2x + 7

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

y = x² + 2(1)x + 1 - 1 + 7

= (x + 1)² + 6 ← in vertex form

Answer 2

( 1, 6 )

Explanation:

y = (x − 1 ) 2 + 6

Use the vertex form, y = a ( x − h ) 2 + k , to determine the values of a , h , and k . a = 1 h = 1 k = 6

Find the vertex ( h , k ) . ( 1 , 6)