APEX Chapter 3 Quadratic Functions

Teacher's Guide  |  PDF

Published on 2014 October 9th

In this chapter, we'll expand our exploration of functions and relationships to include non-linear functions: quadratic functions
At the end of Chapter 3, the learners should be able to demonstrate knowledge and skills related to quadratic functions and apply it to business and industry.
Specifically they should be able to:
1. identify quadratic function f(x) = ax2 + b x + c;
2. rewrite a quadratic function ax2 + bx + c in the form f(x) = a(x-h)2 + k and vice versa;
3. determine the highest or lowest point (vertex), axis of symmetry and direction of opening of the graph given a quadratic function;
4. draw the graph of a quadratic function using the:
? vertex
? axis of symmetry
? direction of opening of the graph
? given points
5. analyze the effects on the graph of changes in a, h and k in f(x) in
(f(x) = a(x-h)2+k;
6. determine the zeroes of a quadratic equation? by relating this to ? roots of a quadratic equation?;
7. find the roots of a quadratic equation by factoring, quadratic formula and completing the square;
8. derive a quadratic function given zeroes of the function, table of values and graph;
9. solve problems involving quadratic functions and equations.

Curriculum Information

K to 12
Grade 9
Patterns and Algebra
Illustrates quadratic equations Solves quadratic equations by a extracting square roots b factoring c completing the square and d using the quadratic formula Characterizes the roots of a quadratic equation using the discriminant Describes the relationship between the coefficients and the roots of a quadratic equation Solves equations transformable to quadratic equations including rational algebraic equations Solves problems involving quadratic equations and rational algebraic equations Illustrates quadratic inequalities Solves quadratic inequalities Solves problems involving quadratic inequalities Models reallife situations using quadratic functions Represents a quadratic function using a table of values b graph and c equation Transforms the quadratic function defined byy ax2 plus bx plus cinto the formy ax h2 k Graphs a quadratic function a domain b range c intercepts d axis of symmetry e vertex f direction of the opening of the parabola Analyzes the effects of changing the values of a h and k in the equation y ax h2 plus k of a quadratic function on its graph Determines the equation of a quadratic function given a a table of values b graph c zeros Solves problems involving quadratic functions Illustrates situations that involve the following variations a direct b inverse c joint d combined Translates into variation statement a relationship between two quantities given by a a table of values b a mathematical equation c a graph and vice versa Solves problems involving variation Applies the laws involving positive integral exponents to zero and negative integral exponents Illustrates expressions with rational exponents Simplifies expressions with rational exponents Writes expressions with rational exponents as radicals and vice versa Derives the laws of radicals Simplifies radical expressions using the laws of radicals Performs operations on radical expressions Solves equations involving radical expressions Solves problems involving radicals

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