 34 lessons
 0 quizzes
 7 week duration

Unit 1: Linear Systems

Unit 2: Analytic Geometry

Unit 3: Geometric Properties

Unit 4: Quadratic Relations
Most relations that you have studied in mathematics have been linear. However, many nonlinear also exist in real life.

Unit 5: Quadratic Expressions

Unit 6: Quadratic Equations

Unit 7: Trigonometry
Transformations of Quadratics
The simplest quadratic equation is:
y = x²
If you were to graph this using a table of values, it would look like the graph on the left.
Notice that vertex is directly at (0, 0). But a world where all parabolas are fixated at the origin would be boring. In this lesson, we will learn how to move quadratic around the xy plane algebraically. This is known as transforming a quadratic equation.
Let’s see what happens with we add or subtract a constant, c, to y = x² ± c.
 Note that some textbooks use “k” to denote the constant!
The takehome message is:
To graph y = x² ± c, translate the graph of y = x² vertically c units.
 If c > 0, then the graph is translated upwards by c units.
 If c < 0, then the graph is translated downwards by c units.
Next we’ll look at what happens when we manipulate the acoefficient, y = ax².
The first video will show you how a +positive acoefficient affects the stretching/compressing of the parabola. Two example are provided, so be sure watch both examples!
If you’d like to reflect the quadratic, so that it’s facing down, make the acoefficient –negative.
The takehome message is:
To graph y = ax², stretch or compress the graph of y = x² vertically by a factor of a.
 If a < 0, the parabola is reflected in the xaxis (a frown).
 If a > 1 or a < –1, then the graph is stretched vertically (narrows).
 If –1 < a < 1 (and a ≠ 0), then the graph is compressed vertically (widens).
Finally, in order to translate the parabola left and right from the origin, a constant, h, must be added or subtracted to the initial xterm, like this: y = (x ± h)².
The takehome message is:
To graph y = (x ± h)², translate the graph of y = x² horizontally h units.
 If h > 0, then the graph is translated h units to the right.
 If h < 0, then the graph is translated h units to the left.