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  1. • Create a quadratic equation given a graph or the zeros of a function. Learning Target #3: Solving by Non Factoring Methods • Solve a quadratic equation by finding square roots. • Solve a quadratic equation by completing the square. • Solve a quadratic equation by using the Quadratic Formula.

  2. This topic introduces quadratic functions, their graphs and their important characteristics. Quadratic functions are widely used in mathematics and statistics. They are found in applied and theoretical mathematics, and are used to model non-linear relationships between variables in statistics.

  3. Quadratic functions are of the form y = ax 2 + bx + c (where a ≠ 0 ) and they have interesting properties that make them behave very differently from linear functions. interesting symmetry. Studying quadratics offers a route into thinking about more complicated functions such as y = 7 x 5 −.

  4. Quadratic Functions Review 1. Properties of Quadratics 2. Converting Between Forms (Expanding and Factoring) 3. Finding the Zeros 4. Determining the Number of Zeros (Discriminant, Signs of a and k) 5. Max/Min Values 6. Word Problems 7. Write the Equation 8. Solving Linear­Quadratic Systems 9. The 4 Transformations

  5. Understand the relationship between a graph of a quadratic function and its associated algebraic equation, and use the relationship between points of intersection of graphs and solutions of equations. 1.1 Solving quadratic equations by factorisation . WORKED EXAMPLE 1.1 . PS. speed of x km/h . His average speed for the return

  6. An algebraic expression can change signs only at the x-values that make the expression zero or undefined. The zeros and undefined values make up the critical numbers of the expression, and they are used to determine the test intervals in solving quadratic and rational inequalities.

  7. To solve a quadratic equation by graphing, first write the equation in standard form, ax2 1 bx 1 c 5 0. Then graph the related function. y 5 ax2 1 bx 1 c. The x-intercepts of the graph are the solutions, or roots, of ax2 1 bx 1 c 5 0.

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