Question

Write the quadratic function in vertex form.

y = x^2 + 4x + 7

Answer 1

Complete the square for the x terms

y = x^2 + 4x + 7

y + 4 = x^2 + 4x + 7 + 4 ... see note below

y + 4 = (x^2 + 4x + 4) + 7

y + 4 = (x+2)^2 + 7

y = (x+2)^2 + 7-4

y = (x+2)^2 + 3


Note: you take half of the x coordinate 4 to get 2, then you square 2 to get 4. Then you add this to both sides

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So

y = x^2 + 4x + 7

turns into

y = (x+2)^2 + 3

which is now in vertex form

Answer 2

y = (x+2)^2 + 3

is in the form

y = a(x-h)^2 + k

where

a = 1
h = -2
k = 3

So the vertex is (-2, 3)