Question

What is the vertex of the graph of y + 2x + 3 = –(x + 2)2 + 1? (–3, –33) (–3, 3) (3, –24) (3, 21)

Answer 1

Explanation:

the answer is -3,3

Answer 2

ANSWER

(-3,3)

EXPLANATION

The given function is


`y + 2x + 3 = - (x + 2) ^(2) + 1`

Expand


`y + 2x + 3 = - x ^(2) - 4x - 4 + 1`

Rewrite in the form:


`y =a {x}^(2) + bx + c`

This implies that,


`y = - x ^(2) - 4x - 2 x - 4 + 1 - 3`


`y = - {x}^(2) - 6x - 6`

Complete the square to get,


`y = - ( {x}^(2) + 6x) - 6`


`y = - ( {x}^(2) + 6x + {(3)}^(2) ) - - {(3)}^(2) - 6`


`y = - {(x + 3)}^(2) +9 - 6`


`y = - {(x + 3)}^(2) +3`

The function is now in the form:


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

where (h,k) =(-3,3) is the vertex