Presentation on theme: "Chapter 9: Quadratic Equations and Functions"— Presentation transcript:
1Chapter 9: Quadratic Equations and Functions Lesson 4: Quadratics and ProjectilesMrs. Parziale
2Vocabulary:objectprojectile: is an ______________ that is thrown, dropped, or launched, and then proceeds with no additional force on its own.
3c 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-interceptcupdownminimummaximum
4Properties 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 ________.vertextimeheightzero
5General 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)
6Example 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)
7Example 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?
8Example 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)
9ClosureWhat 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?