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

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

Answer 2

Answer:

Step-by-step explanation:

the answer is -3,3