1. Chapter 9: Quadratic Equations and Functions
Lesson 4: Quadratics and Projectiles
Mrs. Parziale

2. Vocabulary:
object
projectile: is an ______________ that is thrown, dropped, or launched, and then proceeds with no additional force on its own.

3. c Rules or Properties: y-intercept up down minimum maximum
In the equation y = ax2 + bx + c the initial value or starting point is the _____________ which is the _______ value.
The coefficient a determines whether the graph opens ________ or ______________.
The vertex is a _______________ on a graph that opens upward and a _________________ on a graph that opens downward.
y-intercept c up
down
minimum
maximum

4. Properties vertex time height zero
In a projectile problem, the object being projected reaches a maximum height at its _________.
The x-coordinate represents _______________ the projectile travels.
The y-coordinate represents _______________ the projectile is from the ground.
When the projectile reaches the ground, the y-coordinate is ________.
vertex
time
height
zero

5. General Formula for the height of a Projectile over Time:
where h = height (feet), t = time, v = initial velocity, s = initial height (ft)
where h = height (meters), t = time, v = initial velocity, s = initial height (meters)

6. Example 1:
A ball is thrown from an initial height of 6 feet with an initial upward velocity of 32 feet per second.
a) Write a formula describing the height of the object (in feet) after t seconds.
b) How high will the ball be ½ second after it is thrown?
   
c) What is the maximum height this ball reaches? (vertex – use the MAXIMUM function on calculator)
d) When does the ball reach the ground? (x-intercepts – use the ZEROS function on calculator) 

7. Example 2: An object is dropped from an initial height of 90 meters.
What is the initial velocity?
Write a formula describing the height of the object (in meters) after t seconds. 
After how many seconds does the object hit the ground? Set the equation equal to zero and solve for t.   
What is the maximum height of the object? 

8. Example 3:
Suppose a ball is thrown upward with an initial velocity of 22 meters per second from an initial height of 2 meters.
Write a formula describing the height of the object (in meters) after t seconds.
What is the y-intercept?
What are the x-intercepts?
What do the x-intercepts imply?
Estimate when the ball is 20 meters high. (graph a horizontal line y=20 and use the INTERSECT function on the calculator)

9. Closure
What is the formula used to find the height of a projectile over time?
What does the “c” value represent?
How do you find the x-intercepts?
What do the x-intercepts represent?
Setup this situation: A ball is batted with an initial upward velocity of 26 meters from an initial height of 1 meter. When is the ball 5 meters high?