Alg II Unit 4-5 Quadratic Equations

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Alg II Unit 4-5 Quadratic Equations

  1. 1. 4-5 QUADRATIC EQUATIONSChapter 4 Quadratic Functions and Equations©Tentinger
  2. 2. ESSENTIAL UNDERSTANDING ANDOBJECTIVES Essential Understanding: Standard Form: to find zeros of a quadratic function y = ax2 + bx + c, solve the related quadratic equation = ax2 + bx + c Objectives: Students will be able to:  Solve quadratic equations by factoring  Solve quadratic equations by graphing
  3. 3. IOWA CORE CURRICULUM Algebra A.SSE.1a. Interpret parts of an expressions, such as terms, factors, and coefficients A.APR.3. Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. A.CED.1. Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (concept byte)
  4. 4. ZERO What do you think when I say the zero of a function? Zero of a function is where the graph crosses the x- axis. You can solve quadratic equations in standard form by factoring, using the zero product property Zero product property: if ab = 0, then a = 0 or b = 0
  5. 5. EXAMPLE Solving a Quadratic Equation by Factoring What is the solution to: x2 – 7x +12 = 0 x2 + 3x -18 = 0
  6. 6. EXAMPLE Solving by Graphing What is the solution to: 4x2 – 14x + 7 = 4 – x x2 +2x = 24
  7. 7.  The function y = -0.03x2 + 1.6x models the path of a kicked soccer ball. The height is y, the distance is x, and the units are in meters. How far does the soccer ball travel? How high does the soccer ball go? Describe a reasonable domain and range for the function.
  8. 8. HOMEWORK Pg. 229 – 230 # 9 – 14, 33 – 36, 41, 47 – 52, 59

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