3.7.5Practice:Modeling: Pumpkin Launch

Practice

Algebra II Sem 1

Points Possible:20

Name:Sroth Sinha

Date:

Use the questions below to keep track of key concepts from this lesson's study activity.

YOUR ASSIGNMENT: Splatapults Away!

The engineering club has built a catapult and wants to test it out. The local supermarket has donated some overripe fruits and vegetables, and now the club is holding a Splatapult challenge to see who can hit the most targets. The catapult can launch food pretty far and make a real mess! In order to hit a target and win the Splatapult challenge, you'll need to aim the catapult just right. Use the Graphing Tool and your knowledge of quadratic functions to help you model the flight paths of the different projectiles and hit the target.

Organize your information

1. Which fruit or vegetable did you select? List the information you know about its path.(2 points: 1 point for the selection, 1 point for the values)

2. Your fruit or vegetable will follow a parabolic path, wherexis the horizontal distance it travels (feet), andyis the vertical distance (feet).

a) Thex-intercepts are the places where your fruit or vegetable is on the ground.

The firstx-intercept is (0, 0).

The secondx-intercept is where the fruit or vegetable hits the ground after it's launched.

What are the coordinates of the secondx-intercept?(2 points: 1 point for each coordinate)

b) Which point on the parabola shows the maximum height of your fruit or vegetable?(1 point)

c) Thex-coordinate of the vertex is halfway between thex-coordinates of the endpoints. They-value of the vertex is the maximum height of the fruit or vegetable. What are the coordinates of the vertex?(2 points: 1 point for each coordinate)

3. Use the information above to sketch the flight path of your projectile.(2 points)

4. Label thex-intercepts and vertex on your sketch.(3 points: 1 point for each correct point)

Writing the equation

Complete questions 5 - 8 to write a quadratic equation for the parabola.

5. Using the coordinates of thex-intercepts, what are the two roots of your quadratic equation?(1 point: point for each root)

Hint: The roots are the same as the zeros (thex-values of thex-intercepts).

r₁= _____r₂= _____

6. Substitute the roots from question 5 into the equationy=a(x-r₁)(x-r₂).(2 points)

7. Substitute the coordinates of the vertex forxandyin the equation from question 6. Solve the equation fora.(2 points)

8. Using the value ofafrom question 7, write the quadratic equation in the formy=a(x-r ₁)(x-r ₂).(1 point)

9. Using the distributive property, multiply the equation in question 8 to get the quadratic equation in the formy=ax²+bx.(1 point)

10. Use the Graphing Tool to create a parabola with your vertex andx-intercepts.

• To use the graphing tool, first zoom out to get the scale you want.
• Select the parabola, "U", button.
• The click the point that you want as the vertex.
• Then click the origin (0, 0).

The Graphing Tool will give you an equation for the function you have created. This equation should be close to the equation from question 8. Write the equation here:(1 point)