1 / 11

QUADRATIC EQUATIONS

QUADRATIC EQUATIONS. PROBLEM SOLVING. WARM UP. Find the equation of the axis of symmetry and the co-ordinates of the vertex point of the function: y – 2x² + 10x – 7 Graph the function: f(x) = x² + 6x + 5 Use your graphing calculator and graph the following function: y = ½ x² + 4x + 1

louis
Download Presentation

QUADRATIC EQUATIONS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. QUADRATIC EQUATIONS PROBLEM SOLVING

  2. WARM UP Find the equation of the axis of symmetry and the co-ordinates of the vertex point of the function: y – 2x² + 10x – 7 Graph the function: f(x) = x² + 6x + 5 Use your graphing calculator and graph the following function: y = ½ x² + 4x + 1 a. What is the axis of symmetry? b. What is the co-ordinates of the vertex? c. What are the roots? d. Now graph your points.

  3. PROJECTILE MOTION What is projectile motion? Projectile motion is a form of motion in which an object is thrown, dropped or shot and then moves along a curved path under the action of gravity. The path followed by a projectile motion is called the trajectory.

  4. These problems use a function to represent the object’s height which depends on: • The force of the gravity pulling it down (always -16 when dealing with ft/sec on the squared term). • The initial velocity at which it was thrown/dropped (always goes with the middle term). • The initial height from which it was thrown/dropped. h = - 16t² + vt + c Where t is the time in motion ( in seconds), v is the initial upward velocity (in feet per second), and c is the initial height (in feet).

  5. How long to reach the maximum height: find the axis of symmetry How far off the ground at its maximum height: y value of the vertex When it would hit the ground: roots

  6. An object is launched directly upward at 64 feet per second from a platform 80 feet high. • Write a function to represent this situation. • Graph the function. • When will the object reach its maximum height? (What is really being asked?) • What will the maximum height be? (What is this really asking?)

  7. Zen throws a ball upward with an initial upward velocity of 64 ft/s. The ball is 5 feet above the ground when it leaves Zen’s hand. • In how many seconds will the ball reach its maximum height? • What is the ball’s maximum height?

  8. A fireworks rocket is shot upward with an initial velocity of 80 ft/s. The rocket is 3 feet above the ground when it is fired. • In how many seconds will the rocket reach its maximum height? • What is the rocket’s maximum height?

  9. Chase stands on his garage and kicks a soccer ball with an upward velocity of 60 feet per second. When the ball leaves his foot, it is 25 feet above his driveway. • Write an equation for the situation. • How long does it take the ball to reach its maximum height? • How high does the ball get? • How long does it take the ball to land on the driveway?

  10. Tiger Woods hits a golf ball with an initial upward velocity of 29.4 meters per second (we are not calculating distance, only height and time). The golf ball lands on the green, with is 12 meters below the tee box (use this for the initial height, the tee box is 12 meters above the green). • Write an equation for this situation. • How long does it take the ball to reach its maximum height above green? • How high does the ball get? • How long does it take the ball to land on the green? • How high above the green is the ball after 4 seconds? • How high above the green is the ball after 6 seconds?

  11. Ashely fires a small rocket in her backyard with an initial upward velocity of 78.4 meters per second. The rocket launches from ground level. • Write an equation for this situation. • How high will the rocket be after 4 seconds? • How long does it take the rocket to reach its maximum height? • How high will the rocket get? • How long will it take land?

More Related