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

y = (x + 1) ² + 6

Step-by-step 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

(1, 6)

Step-by-step 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)