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

Solution:

y + 2x + 3 = -(x + 2)² + 1 [Given]

The vertex of the parabola, which is denoted as the coordinates (h, k).

The standard equation of the parabola is y = a(x-h)² + k

The given equation can be written as

y = -(x + 2)² + 1 - 2x - 3

Expand using the algebraic identity (a + b)² = a² + b² + 2ab

y = - (x² + 4 + 4x) + 1 - 2x - 3

y = -x² - 4 - 4x - 2x - 2

By further calculation

y = - x² - 6x - 6

Taking negative sign common in the first two terms

y = - (x² + 6x) - 6

Now add and subtract 9 on the RHS using completing the square.

y = - (x² + 6x + 9 - 9) - 6

So we get

y = - (x + 3)² + 3

y = - (x - (-3))² + 3

Vertex = (-3, 3)

Therefore, the vertex of the graph is (-3, 3).

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

Summary:
The vertex of the graph of y + 2x + 3 = -(x + 2)² + 1 is (-3, 3).