Mathematics

Grade Levels: 11th Grade, 12th Grade,

Topics: MathematicsAlgebra 2Parabolas

Common Core State Standard: 8.F.1, F-IF.1, F-IF.7a, F-IF.7b, F-IF.7c,

Concepts:

· Quadratic equations and graphing quadratic equations

Knowledge and Skills:· Knowledge of quadratic equations and parabolas

· Knowledge of the roots of a quadratic equation

· Knowledge of the vertex (maximum, minimum) of a parabola

Paper and pencil

Watch The Futures Channel video – “Mars Helicopter: Ingenuity”

Download the Teacher Guide PDFDownload the Student PDFLesson:

Procedure: This project should be done by students individually.

NOTE: The following lesson can be done during class as a teacher-led class

lesson for an example of how parabolas and parabolic paths are used in real life,

or the following lesson can be passed out as homework if the students are

already proficient at working with parabolas and graphing them.

**STUDENT HANDOUT**

**INTRODUCTION:**

You are part of the NASA team tasked with controlling the Mars

Helicopter: Ingenuity. From your station in the control room, the

helicopter can be moves from location to location around the surface

of Mars, feeding valuable information back to Earth. Today, Ingenuity

has sent an image of a large range of Mars mountains right in front of

it. You will need to safely fly Ingenuity over the mountain range to the

other side. Luckily, satellite imagery tells you how high and wide this

range is. From the data the satellite has given you, the range’s highest

point is 6,184 ft. The width of the mountains to flat land on the other

side is 3 miles. Your team has been crunching the numbers and believes

they have an equation which will safely carry Ingenuity across the

mountain range.

They have presented you with the equation: f(x) = – 0.00008×2 + x.

**ANSWER THE FOLLOWING QUESTIONS:**

1. Will the above equation provide a safe path for Ingenuity to land on

flat ground? Yes or No? If no, tell whether it is a problem of

height or a problem of distance.

2. Graph the quadratic equation f(x) = – 0.00008×2 + x to support you

claims. Show why the team’s equation works or does not work.