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• EQUATIONS & INEQUALITIES ONE VARIABLE
• LINEAR EQUATIONS
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 UNIT I EQUATIONS AND INEQUALITIES IN ONE VARIABLE Expressions and Formulas: You will have opportunity to practice order of operations in geometric formulas, and up to the quadratic formula that demands better command of these rules. Real Numbers: In order for you to be able to work in the following sections of this algebra one course, you will have to know the different number sets. All complex numbers are real numbers, but not all real numbers are complex numbers. Or you could say all integers are real numbers, but not all real numbers are integers. Additionally, a review of properties for real numbers is given. The interpretation of the narratives for word problems, and directions further in the book will be easier to understand if you know these concepts. Equations, Including Absolute Value Equations: When you have to solve an equation, you need to decide if you have to add, subtract, multiply, or divide a given term in the equation. You have to do it in both sides of the equation; not to alter the value of the equation. This requires to have a good command of the properties of equality. Solving inequalities is almost the same, except that you deal with multiple solutions for the same variable. Learn to use the properties of equality to solve one variable linear equations and inequalities. Inequalities and Absolute Value Inequalities: If you have to decide what may be the length of a third side in a triangle if they give you two of the sides, then mentally you will try to find it by knowing that this third side needs to be more than the other two sides together, otherwise you can't form the triangle. If they are less, the triangle doesn't "close", if you make it equal then you have two parallel lines tightly together. At the same time, if you choose it too long then the triangle won't "close" for the same reason that when you chose it too short, but now with the new side. This problem is a geometric problem that is solved with three compound inequalities made when you state adding two of the sides more than the third side, and allowing each one of the sides to be the third side in one of the three inequalities. Learn to apply the properties of inequality to solve inequalities and absolute value inequalities.

 UNIT IV QUADRATIC FUNCTIONS Quadratic Functions and Its Roots. In algebra one you don't deal with the general equation for conics that may have as geometric space (graph) a circle, a parabola, a hyperbola, or a ellipse. You just deal with a second degree polynomial in the right side of the equation that has as geometric space, the parabola. Nevertheless, to find the zeros, roots, solutions, or x-intercepts; you need to solve quadratic functions using several methods. For example: By factoring, completing the square and by use of the Quadratic Formula. This presentation dwells in each one of them with morbid attention to detail in order to help you not to miss, what you might have missed before. Discriminant, Product and Sum of Roots. If you graph a parabola just by selecting a feasible domain to display it with vertex and whether it opens up or down, right or left. Then you will discover that sometimes it intersects the x-axis in two points, sometimes in only one, and sometimes it does not intersect at all (vertical parabolas). You are going to have the ability at the end of this lesson to determine the number of roots of a quadratic equation by looking at the radicand of the quadratic formula, and evaluating it to determine if is more, equal, or less than zero. This in turn will tell you if the parabola will intersect in two points, one, or none the x-axis. Additionally, you will practice how to verify the solution with the product and sum of its roots.