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Vertex Form

Vertex Form. Monday, April 14 th. Vertex form. What is the vertex (max or min point) of the function: y = –5x 2 + 4? Maximum = (0, 4) Minimum = (0, 4) Maximum = (4, 0) Minimum = (4, 0). Vertex form. What is the vertex (max or min point) of the function: y = –5x 2 + 4? Maximum = (0, 4)

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Vertex Form

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  1. Vertex Form Monday, April 14th

  2. Vertex form What is the vertex (max or min point) of the function: y = –5x2 + 4? • Maximum = (0, 4) • Minimum = (0, 4) • Maximum = (4, 0) • Minimum = (4, 0)

  3. Vertex form What is the vertex (max or min point) of the function: y = –5x2 + 4? • Maximum = (0, 4) • Minimum = (0, 4) • Maximum = (4, 0) • Minimum = (4, 0)

  4. Vertex form What is the vertex (max or min point) of the function: y = 3x2 + 4? • Maximum = (0, 4) • Minimum = (0, 4) • Maximum = (4, 0) • Minimum = (4, 0)

  5. Vertex form What is the vertex (max or min point) of the function: y = 3x2 + 4? • Maximum = (0, 4) • Minimum = (0, 4) • Maximum = (4, 0) • Minimum = (4, 0)

  6. Vertex form y = a(x)2 + k Vertex is (0, k)

  7. Vertex form y = a(x – h)2 + k Vertex is (h, k)

  8. Vertex form y = -0.5(x – 2)2 + 3 Vertex is (2, 3)

  9. Vertex form What is the vertex (max or min point) of the function: y = 3(x – 5)2 + 4? • Maximum = (-5, 4) • Maximum = (3, 4) • Minimum = (-5, 4) • Minimum = (5, 4)

  10. Vertex form What is the vertex (max or min point) of the function: y = 3(x – 5)2 + 4? • Maximum = (-5, 4) • Maximum = (3, 4) • Minimum = (-5, 4) • Minimum = (5, 4)

  11. Vertex form What is the vertex (max or min point) of the function: y = 2(x + 3)2 + 4? • Maximum = (-3, 4) • Maximum = (3, 4) • Minimum = (-3, 4) • Minimum = (3, 4)

  12. Vertex form What is the vertex (max or min point) of the function: y = 2(x + 3)2 + 4? • Maximum = (-3, 4) • Maximum = (3, 4) • Minimum = (-3, 4) • Minimum = (3, 4)

  13. Vertex form What is the vertex (max or min point) of the function: y = –½(x + 7)2 + 4? • Maximum = (-7, 4) • Maximum = (7, 4) • Minimum = (-7, 4) • Minimum = (7, 4)

  14. Vertex form What is the vertex (max or min point) of the function: y = –½(x + 7)2 + 4? • Maximum = (-7, 4) • Maximum = (7, 4) • Minimum = (-7, 4) • Minimum = (7, 4)

  15. Ms. Breimer leaps from her stair to the ground during her epic dash to teach you! MsBreimer reaches a max height of 2.5m after 0.32s. At 0s, she stands on the 2m high stair case. What is her height above the ground as a function of time?

  16. MsBreimer reaches a max height of 2.5m after 0.32s. At 0s, she stands on the 2m high stair case. y (0.32, 2.5) y = a(t – h)2 + k y = a(t – 0.32)2 + 2.5 (0, 2) What is a? Plug in a point! (0, 2) 2 = a(0 – 0.32)2 + 2.5 2 = a(0.1024) + 2.5 t 2 – 2.5 = a(0.1024) a = –4.9

  17. If MsBreimer reaches a max height of 2.5m after 0.32s. At 0s, she stands on the 2m high stair case. y (0.32, 2.5) The equation for Ms. Breimers height above the ground as a function of time is: y = –4.9(t – 0.32)2 + 2.5 t

  18. If MsBreimer reaches a max height of 2.5m after 0.32s. At 0s, she stands on the 2m high stair case. y (0.32, 2.5) y = –4.9(t – 0.32)2 + 2.5 From this equation, we can figure out if Ms. Breimer is on earth or another planet, what her initial jump velocity was, and much more! t

  19. Using the quadratic equation y = –4.9(t – 0.32)2 + 2.5 Put this in standard format: y = Ax2 + bx + c

  20. Using the quadratic equation y = –4.9(t – 0.32)2 + 2.5 Put this in standard format: y = –4.9t2 + 3.1t + 2

  21. Using the quadratic equation y = –4.9(t – 0.32)2 + 2.5 Put this in standard format: y = –4.9t2 + 3.1t + 2 Compare this to the equation for height: y2 = ½gt2 + v1t + y1 y2 = the height above the ground after some time, t g = the acceleration due to gravity (this is –9.8m/s2 on earth and –1.6m/s2 on the moon) v2 = the initial velocity y1 = the initial height off the ground

  22. Using the quadratic equation y = –4.9(t – 0.32)2 + 2.5 Put this in standard format: y = –4.9t2 + 3.1t + 2 Compare this to the equation for height: y2 = ½gt2 + v1t + y1 ½g = -4.9 Ms. Breimer is on a planet with earth’s gravity g = -9.8

  23. Using the quadratic equation y = –4.9(t – 0.32)2 + 2.5 Put this in standard format: y = –4.9t2 + 3.1t + 2 Compare this to the equation for height: y2 = ½gt2 + v1t + y1 v1 = 3.1 Ms. Breimer jumped with an initial velocity of 3.1m/s

  24. Using the quadratic equation y = –4.9(t – 0.32)2 + 2.5 Put this in standard format: y = –4.9t2 + 3.1t + 2 Compare this to the equation for height: y2 = ½gt2 + v1t + y1 y1 = 2 Our staircase is 2m high

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