· Quadratic equations and graphing quadratic equations

· 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”

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.