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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. The module covers the algebra and graphing skills needed for analysing and using quadratic functions. Author of Topic 3: Paul Andrew __
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.
1 Quadratic Functions. In this unit we will learn many of the algebraic techniques used to work with the quadratic function. f(x) = ax2 + bx + c: 1.1 Completing the Square. lled completing the square is the way that we can isolate the variable x in a general quadratic. You will see this process aga.
Quadratic Functions. . Definition: If a, b, c, h, and k are real numbers with a 6= 0, then the functions. y = ax2 + bx + c. standard form. y = a(x − h)2 + k. vertex form. both represent a quadratic function. The graph of a quadratic function is called a parabola.
In this Module learners explore and analyse the characteristics of the quadratic function y = a x 2 + b x + c and the effect of the parameters a, b and c on the behaviour of the function and form of the graph of the function.
For example, fireworks, when fired, follow a parabolic path and many explode when the vertex is reached. This unit will introduce you to quadratic functions. In addition, you will solve quadratic equations using factoring and the Zero Product Property.
2.1 explain the meaning of the term function, and distinguish a function from a relation that is not a function, through investigation of linear and quadratic relations using a variety of representations (i.e., tables of values, mapping diagrams, graphs, function machines, equations) and strategies. 2.2 substitute into and evaluate linear and ...
