Question

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

Answer 1

Answer:

  (-3, 3)

Step-by-step explanation:

A graphing calculator shows the vertex to be (-3, 3).

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You can rearrange the equation to vertex form:

  y +2x +3 = -(x +2)^2 +1

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

  y = -x^2 -6x -6 . . . . . . . . . . . . .collect terms

  y = -(x^2 +6x) -6 . . . . . . . . . . . factor first pair

  y = -(x^2 +6x +9) -6 +9 . . . . . add and subtract -9

  y = -(x +3)^2 +3 . . . . . . . . . . . vertex form

In vertex form y=a(x-h)^2+k, the vertex is (h, k). Here, that is (-3, 3).

The vertex of the graph of this equation will be at point (x, y) = (-3, 3).