# MAT 085 - Quadratic Equations and Circles Simplify square roots of non-square numbers and variable expressions. Solve quadratic equations by factoring, the square root property, completing the square, and the quadratic formula. Graph a parabola by finding the vertex, intercepts, and axis of symmetry. Graph a circle given its equation. Use completing the square to graph circles and parabolas. Compare the graphing traits of functions and non-functions. Apply the vertical line test. Determine the range of a function. Solve application problems with quadratic equations.
**Prerequisite- Corequisite** Prerequisite: MAT 084 Polynomials
Credits: 0
**Hours** 1 Class Hour
**Course Profile** Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Simplify square roots of non-square numbers.
2. Simplify square roots of variable expressions.
3. Solve quadratic equations by factoring and the square root property.
4. Solve quadratic equations by completing the square.
5. Solve quadratic equations by using the quadratic formula.
6. Find the vertex and axis of symmetry of a parabola.
7. Graph a parabola by finding the vertex, intercepts, and additional points.
8. Graph a circle given its equation in standard or general form.
9. Use completing the square to graph circles and parabolas.
10. Compare the graphing traits of functions and non-functions.
11. Apply the vertical line test.
12. Determine the range of a function.
13. Solve application problems with quadratic equations.
In the context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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