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Matching Puzzle

Matching Puzzle. Grab a pair of scissors, a puzzle sheet and sit at your desk. . Warm up: Write the WHOLE problem down.

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Matching Puzzle

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  1. Matching Puzzle Grab a pair of scissors, a puzzle sheet and sit at your desk.

  2. Warm up: Write the WHOLE problem down. The data below represents the height of a rocket shot from 150 ft above ground and traveling at a velocity of 50 m/second. Find the quadratic equation that models this data. 2. What form of the quadratic equation did we get from this data?

  3. Answer: • We can look at this equation and determine a few things about the Projectile Motion Function. • x=time • y=height • a= downward acceleration due to gravity: -4.9 m/ or -16 ft/ • = initial upward velocity • =initial height in meters or feet.

  4. Follow up • Now find the maximum height reached by the rocket, and how many seconds it took to get there. • In order to answer this question we need to know the______? • Can we determine the vertex given the general equation? • What form to we need?

  5. Goal • To convert a quadratic equation from General Form to Vertex Form. • Method: Completing the Square.

  6. Factoring: Completing the Square

  7. General to Vertex form • We want to go from To

  8. Completing the Square Method The two relationships that will allow us to make this conversion are: and

  9. Example 1 • Write in vertex form. • Step 1: identify a,b and c. • a=1, b=-10, c=15

  10. Cont… • Step 2: substitute values into the relations

  11. Cont… • Step 3: Substitute the values for h and k into the vertex form. • Vertex form: • h=5, k=-10, a=1 (never changed) • Solution:

  12. Example 2 • Factor • a=_____, b=______, c=_______ Find h and k. • Plug h and k into • Answer:

  13. State the vertex • What is the vertex of the previous problem? • Answer: (-5,0)

  14. Example 3: You try • What is the vertex of ?

  15. Example 4: You try again • Write the following equation in vertex form.

  16. Example 5 • Write the following equation in vertex form. • Hint: first convert factored form to general form, the change to vertex form)

  17. Example 6 • Find the vertex:

  18. Homework • 7.3: Skip #2 • This is a big assignment. Pace yourself! • The only way to really understand this stuff is to Practice…A LOT!

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