In this resource, you will learn about transformations of quadratic equations. A quadratic equation can be translated up or down, left or right, it can be made wider or narrower, or be made to open up or down. Before we begin, let’s review some basics about quadratic functions.

• A quadratic function is any function whose graph is a parabola.
• A parabola has a “U” shape and opens either up or down.
• A parabola’s shape can be wider (compression), narrower (stretch), or congruent to the parent function.
• An equation of a quadratic function is y = a (x – h)² + k or f(x) = a(x – h)² + k
• x and y represent the x-and y-coordinates of any point (x,y) that lies on the graph of the parabola.
• The constants a, h, and k are called the parameters of the quadratic equation. These constants reveal the shape and location of the parabola.

The most basic quadratic function is y = x². This is also called the parent function of a quadratic function.

Sometimes you will see it written in function notation as f(x) = x².

The graph of y = x² looks like the graph below.

It is called the quadratic parent function because other quadratic functions can be found by transforming y = x².