HSG-GPE.A.2

Math Misconceptions and Considerations HSG-GPE.A.2

Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.

It’s not possible to graph a horizontal parabola on a calculator.

Many students can graph a vertical parabola on a calculator with success.

However, when they use the same method to graph a horizontal parabola they don’t get the correct graph. This occurs because students enter the parabola on the menu incorrectly.

Using a graphing tool, graph the parabola x=( y−4)2 . Most students are able to properly solve this equation for y to obtain an equation formatted for entry into the calculator.

Misconception:

This graph is only showing the positive half of the parabola.

What to do: Unless the calculator is told to graph both the positive and negative halves of the parabola, it will only display one half of the parabola. To remedy this, you must enter both the positive and the negative equations of the parabola as two separate entries.

Interpreting “p” incorrectly Up to this point, students have had little exposure to horizontal parabolas. Due to this fact, students are quick to assume that a negative “p” value implies that the graph opens downward. While this is true in the problems involving a vertical parabola, it is not always the case.

Misconception:

Immediately seeing that the “p” is negative, students may jump to the conclusion that the parabola opens down.

What to do: Do examples with students that vary between horizontal and vertical parabolas and have them determine the value of “p”. Using that value along with other information about the parabola, have students come to conclusions about the parabola. Students will begin to see the relationship between “p”, the orientation of the graph, and the squared variable. Instead of just relying on “p” to determine the direction of the parabola, they will use all of the information imbedded in the equation. The chart below is an example: