Graphing Parabolas: Examples

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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Videos, worksheets, and activities to help Algebra students.
In this lesson, we will learn

  • how to graph a horizontal parabola
  • how to graph parabolas with stretches or dilations
  • how to define the focus and directrix of a parabola

Graphing a Horizontal Parabola

We are used to looking at quadratic equations where “y” is the variable that is equal to the squared “x” terms. However, in a horizontal parabola the “x” is equal to the “y” term squared. Instead of going up and down, a horizontal parabola goes from side to side. When graphing a horizontal parabola, we first need to make sure the formula is in standard form and then plot accordingly.

How to graph a horizontal parabola in vertex form?

Dilations of Quadratic Graphs

When graphing parabolas and other functions, there are certain types of graph dilations that help us graph and explore parabolas more efficiently. When graphing parabolas, dilations occur when the “a” term value is changed. If we change the “a” to a negative, the graph shifts downward instead of upward. As the absolute value of the “a” value increases, the graph becomes “steeper.” If we use a fraction as the “a” value, the graph of the parabola becomes wider.
How to graph parabolas that are wide or skinny or upside down without making a table of values?

Sketching quadratic functions with stretches and flips

Focus and Directrix of a Parabola

A parabola is the curve formed from all points that are equidistant from the directrix and the focus. The parabola focus is a point from which distances are measured in forming a conic and where these distances converge. A parabola directrix is a line from which distances are measured in forming a conic. The line perpendicular to the directrix and passing through the focus is called the axis of symmetry.

How to define the focus and directrix of a parabola?

This video shows that a parabola as the locus of all points equidistant from a point, called the focus, and a line, called the directrix.

Finding the focus and directrix of a parabola

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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