Chapter 5 Objectives:  Quadratic Functions

Section 5.1:  Introduction to Quadratic Functions

Be able to:

-         Define, identify, and graph quadratic functions

-         Multiply linear binomials to produce a quadratic expression

-         Define and graph a parabola, its axis of symmetry, and vertex.

-         Determine whether a quadratic has a maximum or minimum by examining the equation.

-         Approximate coordinates of the vertex and intercepts using a calculator

Section 5.2: Introduction to Solving Quadratic Equations

Be able to:

-         Solve quadratic equations by taking square roots

-         Use the Pythagorean Theorem to solve problems involving right triangles.

-         Apply the product and quotient properties of square roots

-         Simplify square roots and approximate their value with a decimal

Section 5.3:  Factoring Quadratic expressions

Be able to:

-         Factor a quadratic expression

-         Identify special expressions such as the difference of two squares, and perfect-square trinomials

-         Define and apply the “Zero Product Property”

-         Use factoring to solve quadratic equations and find the zeros of a quadratic function.

Section 5.4:  Completing the Square

Be able to:

-         Use completing the square to solve a quadratic equation

-         Write a quadratic function in vertex form using completing the square.

-         Use the vertex form (turning point form) of a quadratic function to locate the axis of symmetry of its graph.

-         Describe how the graph of an equation in vertex form is related to the graph of  using transformations.

Section 5.5:  The Quadratic Formula

Be able to:

-         Use the quadratic formula to find real roots of quadratic equations.

-         Use the formula x = -b/(2a) to locate the axis of symmetry and vertex of a parabola.

Section 5.6:  Quadratic Equations and Complex Numbers

Be able to:

-         Use the discriminant test to classify the nature of the roots of a quadratic equation.

-         Define imaginary numbers and complex numbers

-         Find the real and imaginary parts of a complex number.

-         Simplify expressions containing complex numbers by writing them in  form.

-         Define the complex conjugate of a number.

-         Graph complex numbers.

-         Find  for any complex number and understand what this number represents on a graph.

Objectives for 5.6 and 5.7 will be added at a later time.