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Quadratic Functions Exploration Guide

Study and explore quadratic functions and operations on functions, including polynomial and quadratic functions, standard form, vertex, roots, discriminant, and word examples. Find areas and solve problems.

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Quadratic Functions Exploration Guide

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  1. Mindjog 10/19 Write a function that will give the area of the garden depending on the dimensions chosen. x x [0,100]by[0,5000] 200-2x

  2. OBJECTIVE • SWBAT • Study and explore quadratic functions and operations on functions.

  3. Polynomial Function • f(x)=anxn+an-1xn-1 +… a1x + a0 • an, an-1,…,a1 and a0 are real #’s, an = 0

  4. Quadratic Function • y = ax2 + bx + c • a, b, and c are real #’s • a ≠ 0

  5. Standard Form • f(x) = a(x – h)2 + k • (h, k) = vertex

  6. Standard Form • f(x) = a(x-h)2 + k • Write in standard form. • f(x) = x2 + 8x – 13 • What do you do???

  7. Try These… • f(x) = a(x-h)2 + k • Write in standard form. • f(x) = 3x2 -18x +40 • f(x) = 4x2 +32x – 10

  8. Other Properties Line of symmetry • x = -b/(2a) = h Vertex • (-b/(2a), c – (b2/4a)) • Or (h, f(h)) Proof on p. 307

  9. Try These… • Find the vertex: • f(x) = 4x2 – 12x +40 • f(x) = 2x2 + 8x – 12

  10. Roots or Zeros • Roots or Zeros means… • The discriminant can help you determine the number of roots and what kind. • Discriminant is…

  11. Discriminant If b2 – 4ac > 0, 2 real roots • If b2 – 4ac = 0, 1 real root, both equal • If b2 – 4ac < 0 then no real roots, 2 imaginary

  12. Discriminant Graphically, this means…

  13. Try These • How many x-intercepts? • f(x) = 2x2 - 4x + 2 • f(x) = -5x2 + 6x + 4 • What are they?

  14. Find the roots • y = x2 + 9x -22 • y = -x2 + 10x - 25

  15. WORD EXAMPLE • Projectile: s(t)= -16t2 + v0t + s0 t = time V0 = initial velocity s0 = initial height

  16. WORD EXAMPLE • A ball is thrown directly upward from an initial height of 100ft with an initial velocity of 80ft/sec.

  17. WORD EXAMPLE a) Graph on calculator b) How long does it take to reach maximum height? What is the maximum height? c) For what interval of time is the height of the ball greater than 160ft? d) After how many seconds will the ball hit the ground?

  18. CLASSWORK • p. 56 #’s 33-51, 59-63, odd

  19. HOMEWORK • p. 311, #’s 2-8 and 12-20 even, 31-36 all, 50, 54, 58

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