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Understanding Quadratic Equations and Projectile Motion

This lesson focuses on solving quadratic equations and analyzing projectile motion using the quadratic formula. Students will answer questions presented on-screen, with correct solutions displayed afterward. If clarification is needed, peers can demonstrate their problem-solving methods using a document camera. We will explore the height of a ball thrown upward, using its initial velocity to determine maximum height and the time it reaches that height. By finding the vertex of the corresponding quadratic function, we identify that the maximum height of the ball is 344 feet, occurring at 3 seconds.

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Understanding Quadratic Equations and Projectile Motion

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  1. Test Review Answer the questions on each screen. The correct answer will be shown on the screen following each question. If someone in the class needs an explanation, someone in the class that worked the problem right can come, show their work under the document camera and explain it to the class.

  2. Use the quadratic formula to solve the equation. 1)

  3. 2) x = 1

  4. 3) x = (-6, 0) and (8, 0)

  5. 4) (-3, -2)

  6. 0

  7. 4

  8. A ball is thrown directly upward from an initial velocity of 96 feet per second. The height of the ball as a function of time can be modeled by the function 14) After how many seconds will the ball reach its maximum height? And, what is the maximum height? Hint: If we are looking for maximum height then we must be finding the vertex.

  9. The axis of symmetry is x = 3. Plug 3 back into the equation for the vertex and you get (3, 344) Therefore the maximum height is 344 feet.

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