Horizontal Translations of Graphs

Discover and Explore Horizontal Translations of Graphs

Scope and Sequence

Ninth Grade: Integrated
Patterns and Relationships #4: Use a graphing calculator or computer to generate the graph of a function.
Tenth Grade: Integrated
Algebra #5: Symbolize transformations of figures and graphs.
Algebra #7: Graph linear functions.
Eleventh Grade: Integrated
Patterns and Relationships #3: Use a graphing calculator or computer to graph functions.

Find a website that can graph equations. Use this site to explore horizontal translations.

1.) Graph the following equations:

a.) y = [x]^(2)
b.) y = [x + 2]^(2)
c.) y = [x - 3]^(2)

Equations such as those above are called quadratic equations. The highest degree variable in a quadratic equation is second degree, or squared. They all resemble the same shape. This shape is called a parabola. The equation graphed in part a is called the parent graph to all parabolas or second degree equations. This is because all quadratic equations are derived from the parent graph. We start with y = [x]^(2) and then by adding / subtracting / multiplying / dividing, we can obtain any other parabola that we wish.