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# What are parent functions and transformations?

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Parent functions are the unmodified form of a family of functions, and parent functions must preserve the shape of the family graph. Modifications to the parent function are transformations. Adding, subtracting, multiplying or dividing by a real number causes a transformation, thus moving or modifying the parent function graph. Parent functions often undergo several transformations.

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The function f(x) = x^2 is the parent quadratic function. Multiplying the function by -1 creates a reflection. The parent function is a parabola that opens upward with its origin at the point (0,0). The graph f(x)=-x^2 has the same origin and shape but opens downward.

Translations slide the function up, down, left or right. The function f(x) = x^2 + b moves the parabola up or down, while f(x) = (x + b)^2 moves it to the left or right. The value of b determines the direction of the move.

Multiplication stretches or compresses the function. Functions go through both horizontal and vertical stretches and compressions depending on the location of the factor. If the factor is between zero and one, the function compresses. If it is larger than one, the function stretches. If the factor is negative, vertical stretches are also reflected over the x-axis and horizontal stretches are reflected over the y-axis.

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