## MTE 9 - Functions, Quadratic Equations and Parabolas at Dabney S. Lancaster Community College

### Course Description

Effective: 2012-01-01

Includes an introduction to functions in ordered pair, graph, and equation form. Also introduces quadratic functions, their properties and their graphs. Credit is not applicable toward graduation.

Lecture 1 hour per week.

1 credits

### General Course Purpose

The purpose of this course is to develop competency necessary to succeed in selected 100-level math courses in solving applications using functions, quadratic functions and their properties.

### Course Prerequisites/Corequisites

Prerequisites: MTE 8 or qualifying placement score.

### Course Objectives

- Determine if a relation is a function and identify the domain and range of the function.
- Determine if a list of ordered pairs, graph, or equation is a function.
- Determine the domain and range of a function given as a list of ordered pairs.
- Determine the domain and range of a function given as a graph.
- Determine the domain of a function given as an equation.
- Evaluate y=f(x) for constant values of x and for specific monomials and binomials.
- Find all roots of quadratic equations using both the square root method and the quadratic formula.
- Find the roots of quadratic equations of the form ax 2 + c = 0 .
- Find the roots of quadratic equations of the form ax 2 + bx + c = 0 when the discriminant is a positive perfect square, (i.e. the quadratic is factorable).
- Find the roots of quadratic equations of the form ax 2 + bx + c = 0 when the discriminant is positive, but not a perfect square.
- Find the roots of quadratic equations of the form ax 2 + bx + c = 0 when the discriminant is zero.
- Find the roots of quadratic equations of the form ax 2 + bx + c = 0 when the discriminant is negative.
- Describe the roots of a quadratic based upon the discriminant in all cases.
- Analyze a quadratic function to determine its vertex by completing the square and using the formula.
- Write a quadratic function in vertex form y=a(x-h)2 + k by completing the square for quadratics with a=1 and identify the vertex (h,k).
- Write a quadratic function in vertex form y=a(x-h)2 + k by completing the square for quadratics with a not equal to 1 and identify the vertex (h,k).
- Find the vertex of a quadratic equation y=ax2 + bx + c using the formula method supplied.
- Graph a quadratic function, using the vertex form, indicating the intercepts and vertex.
- Determine whether the parabola opens upward or downward.
- Plot the vertex of the parabola.
- Determine the axis of symmetry for the parabola.
- Plot the x-intercepts of the parabola, if they exist.
- Plot the y-intercept of the parabola and complete the graph with additional points as needed.
- Apply knowledge of quadratic functions to solve application problems from geometry, economics, applied physics, and other disciplines.
- Solve problems involving area optimization.
- Solve problems involving revenue optimization.
- Solve problems involving the motion of falling objects.

### Major Topics to be Included

- Determine if a relation is a function and identify the domain and range of the function.
- Find all roots of quadratic equations using both the square root method and the quadratic formula.
- Analyze a quadratic function to determine its vertex by completing the square and using the formula.
- Graph a quadratic function, using the vertex form, indicating the intercepts and vertex.
- Apply knowledge of quadratic functions to solve application problems from geometry, economics, applied physics, and other disciplines.