Graphs of Quadratic Equations

Graph of y = ax2 + b

y = 4x2 + 6 is an example of an equation of this type. The basic parabola is y = x2. Multiplying y = x2 by a constant narrows or widens the graph (if the constant is negative, the parabola opens down). Adding a constant shifts the constant up or down.

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Graph of y = a(x - h)2 + k

y = 3(x - 1)2 + 2 is an example of an equation of this type. Replacing x2 by (x - h)2 shifts the parabola horizontally by h units (to the right if h is positive, to the left if h is negative). This is the only difference between this example and the one above.

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Graph of y = ax2 + bx + c

y = 2x2 + 4x + 3 is an example of an equation of this type. We solve equations of this type by completing the square. This reduces the problem to a problem of the previous type.

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