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X^2 + 4X = 0

you must complete the square. halve the coefficient of the linear term (4X) and square it and add it to the other side.

(X + 2)^2 = 4

now subtract the 4 from both sides

(X + 2)^2 - 4 = 0

The graph of y = x2 (vertex (0,0) is shifted 2 units to the left, and 4 units down.

the vertex is....

(-2,-4)

my TI-84 confirms this answer

or

Since x = -4/2 = -2 is the equation of the axis of symmetry, and the vertex lies on it, then the x-coordinate of the vertex is -2 and the y-coordinate is f(-2).

f(-2) = (-2)2 + 4(-2) = 4 - 8 = -4

thus, the vertex is (-2, -4)

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Q: What is the vertex form for y equals x to the secound power plus 4x?
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