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y = X^2 + 4X - 3

set polynomial = to 0

X^2 + 4X - 3 = 0

add 3 to each side

X^2 + 4X = 3

complete the square. take linear term (4) halve it, square it and add constant to other side, factor quadratic term

(X + 2)^2 = 7

subtract 7 from each side

(X + 2) - 7 = 0

Vertex = (-2,-7)

My TI-84 confirms this vertex with original equation

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Q: What is the vertex of y equals x2 plus 4x-3?
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