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Understanding Quadratic Equations and Vertex Form - MT5 EOT Resource

This resource provides a comprehensive guide to solving quadratic equations using methods like completing the square, the quadratic formula, and vertex form. It offers detailed notes and examples to help students understand concepts such as identifying roots, graphing equations in vertex form, and applying gravity formulas in projectile motion problems. The material is suitable for high school Algebra students and serves as a valuable tool for mastering quadratic equations. Enhance your math skills with practical examples and step-by-step solutions for better comprehension.

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Understanding Quadratic Equations and Vertex Form - MT5 EOT Resource

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  1. Score Key for MT5 EOT

  2. 9 9 6.25 6.25 x2 + 6x + ____ = 72 + ____ (x + ____)2 = ____ y = (x + ____)2 - ____ x2 – 5x + ____ = -6 + ____ (x + ____)2 = ____ y = (x + ____)2 - ____ 81 .25 3 2.5 6/2 = 3 5/2 = 2.5 3 81 2.5 .25 Notes: Move “C” to the other side and create “space” for your new numbers. Create ( )2 for you perfect square Find the number to be added to both sides and fill in your spaces. Make your equation look like y = ( )2 + c. This will create “Vertex Form” which will be used in MT6 for graphing.

  3. Score Key for MT5 EOT

  4. 12 -7 -24 2 -4 6 -3 -4 (x )(x ) - 3 - 4 - 4 + 2 6 -4 (3x )(x ) Notes: Diamond method works on both…

  5. Score Key for MT5 EOT

  6. A B C A B C 22 – 4*4*-8 122 – 4*9*4 4 + 128 = 132 144 - 144 = 0 Positive is 2 roots Zero is 1 root Notes: Use b2 – 4ac to find possible roots + is two roots 0 is one root - Is no roots

  7. Score Key for MT5 EOT

  8. -6 ± 62 – 4*2*3 2*2 -13 ± 132 – 4*8*4 2*8 -6 ± 36 – 24 4 -13 ± 169 – 128 16 -6 ± 2 3 4 -3 ± 3 2 -6 ± 12 4 -13 ± 41 16 Notes: Use Quadratic Formula: - b ± b2 – 4ac 2a The negative boy could decide if he wanted to go to the radical party with his two best friends and meet four awesome chicks and be home by two a.m.

  9. Score Key for MT5 EOT

  10. 0 (the ground) 10 seconds ? I have no idea 0 (the ground) Notes: Assign your values to your variables H is ending height T is time V is velocity C is starting height (when you are on the ground, height is 0)

  11. Score Key for MT5 EOT

  12. h = -16(t)2 + v(t) + c 160 0 = -16(10)2 + v(10) + 0 H=0 T=10 V=? C=0 0 = -1600 + 10v 1600 = 10v V=160 Notes: Use gravity formula - h = -16t2 + vt + c, plug in variables, and solve for “V”

  13. Score Key for MT5 EOT

  14. h = -16(t)2 + v(t) + c 5 h = -16(5)2 + 160(5) + 0 400 T=? (Maximum height) h = -400 + 800 H=400 T=0 T=10 Notes: Draw a picture of what is happening. You know velocity (160), you must figure out how many second it took to get to the maximum height. Plug in and solve.

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