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9.3: SOLVING QUADRATIC EQUATIONS:

Quadratic Equation: A function that can be written in the form ax 2 +bx+c = 0 where a ≠ 0. 9.3: SOLVING QUADRATIC EQUATIONS:. Standard Form of a Quadratic: A function written in descending degree order, that is ax 2 +bx+c = 0.

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9.3: SOLVING QUADRATIC EQUATIONS:

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  1. Quadratic Equation: A function that can be written in the form ax2+bx+c = 0 where a ≠ 0. 9.3: SOLVING QUADRATIC EQUATIONS: Standard Form of a Quadratic: A function written in descending degree order, that is ax2+bx+c = 0.

  2. Roots of an equation: the solution of a quadratic equation, the x-intercepts of the graph. Zeros of the function: The x-intercepts of the graph.

  3. GOAL:

  4. The zeros, solutions of the graph are the x-intercepts: Ex: What are the solutions of: A) B) C) FINDING THE ZEROS OF ax2+bx+c:

  5. A parabola could have the following cases: There could be two solutions: in this case: x = -1, and x = 1. SOLUTIONS: There could be one solution: in this case x = 0. There could be no solutions: In this case there are none.

  6. YOU TRY IT: What are the zeros of :

  7. SOLUTION: Here the graph crosses the x axis at the values of: x = -1 x = 2.

  8. When the equation does not include the bx term, we use SQUARE ROOTS: Ex: What are the solutions of: A) m2 – 36 = 0 B) 3x2+15 = 0 C) 4d2+16 = 32 FINDING THE ZEROS OF ax2+ c = 0:

  9. To find the x-intercepts, we must solve for the variable: A) m2 – 36 = 0  m2 = 36  m = m = -6, +6 SOLUTIONS: B) 3x2+15 = 0  3x2 = -15  x2 = -5 x = No solution  4d2 = 0 C) 4d2+16 = 16  d2 = 0  d =  d = 0

  10. REAL-WORLD: You have enough paint to cover an area of 50ft2. What is the side length of the largest square that you could paint? Round your answer to the nearest tenth of a foot.

  11. The area of a square is (side)(side) = s2 Paint covers at most 50ft2 Then: s2= 50ft2 SOLUTION: s= s= ft s= 7.1 ft Notice that length cannot be negative thus s = 7.1 ft

  12. VIDEOS: Quadratic Graphs and Their Properties Solving Quadratics: http://www.khanacademy.org/math/trigonometry/polynomial_and_rational/quad_formula_tutorial/v/solving-quadratic-equations-by-square-roots

  13. CLASSWORK:Page 550-551: Problems: 1, 2, 3, 4, 6, 8, 10, 13, 22, 29, 31, 32, 36, 42.

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