Transformation on a Parabola

Playing around with matrix transformations on algebraic objects. Student page info: Inspired by a sketch from Jen Silverman at [url][/url]. Since a point can be thought of as a 2x1 matrix, a 2x2 matrix can be thought of as a map from the plane R^2 to itself. Because of the properties of matrix multiplication, this is a linear transformation, and linear transformations have a bag full of cool properties. There are at least two ways to think about transforming a parabola, to show the effects of a transformation. The first thinks about the parabola being defined by three points. Transform those, fit a new parabola, and voila, transformed parabola. (Blue in the sketch.) The second shows more what is happening to the whole plane - show the image of every point of the parabola under the transformation. (Green in the sketch.) Play around with the transformation. Can you make a reflection? Can you stretch the plane or compress it?


John Golden

Material Type
matrix  linear  transformation  parabola  quadratic 
Target Group (Age)
15 – 18
English (United States)
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