In this chapter, we'll expand our exploration of functions and relationships to include non-linear functions: quadratic functions
Objective
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
Education Type
K to 12
Grade Level
Grade 9
Learning Area
Mathematics
Content/Topic
Patterns and Algebra
Intended Users
Educators
Competencies
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
