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SUPPORT CENTRE. Title: Quadratic Inequalities. Target: On completion of this worksheet you should be able to solve quadratic inequalities and illustrate the solution set. Quadratic inequalities are inequalities with the highest power of the unknown being two. Examples. 3x. 2. - 2x + 1 > 0 and 4x. 2. + 5x < 7 are quadratic.
Procedure. Solving Quadratic Inequalities. 1. Move all terms to one side. 2. Simplify and factor the quadratic expression. 3. Find the roots of the corresponding quadratic equation. 4. Use the roots to divide the number line into regions. 5. Test each region using theinequality. Example 1. Solve the inequality, x. 2 > x + 2.
The solution set for the inequality is x 3 x 4. x y. When x is between. 3 and 4, f(x) is negative. 12. 6. 6. 6. 12. 12. 12 x y. 12. 6. 6. 6. 12. 12. 12. Algebraic methods can also be used to find the solutions to a quadratic inequality. Sub- sequent examples in this section will discuss algebraic methods. When solving an equation
I. GENERALITIES. There are 3 common methods to solve quadratic inequalities. Therefore, students sometimes are confused to select the fastest and the best solving method. I generally explain below these. 3 methods and then compare them through selected examples. Solving a quadratic inequality, in standard form f(x)
25 Sep 2014 is a parabola. If a > 0, the parabola opens up; if a < 0, the parabola opens down: a > 0 a < 0. You can use the graph of a quadratic function to solve quadratic inequalities. Example. Solve the quadratic inequality x2 ? 2x ? 3 < 0. The graph of f(x) = x2 ? 2x ? 3 opens upward, because the coefficient of x2 is +1.
Page 1. Solving Quadratic Inequalities Algebraically Worksheet. Name. Solve the following quadratic inequalities algebraically. 1) x2 + x – 20 ? 0. 2) x2 – 3x – 54 < 0. 3) x2 – 5x – 14 > 0. 4) 2x2 – 4x – 30 ? 0. 5) 3x2 – 6x – 9 ? 0. 6) 2x2 + 9x – 5 < 0.
I G AA4lHlY QrEiAgNhEtWsR frvecsoe8rJvdecd2.D S 6M7ardWeg qwpiNtkhE yIbnEfLiPnuiGtQem xAXlcgYeibzrPay 82b.j. Worksheet by Kuta Software LLC. Kuta Software - Infinite Algebra 2. Name___________________________________. Period____. Date________________. Quadratic Inequalities. Sketch the graph
solve quadratic inequalities. Contents. 1. Introduction. 2 Quadratic inequalities. 8 www.mathcentre.ac.uk. 1 taken when solving inequalities to make sure you do not multiply or divide by a negative number by accident. For example saying that x>y, implies that x2 > y2 only if x and y are positive. We can see the necessity
and Inequalities. 9.1 Compound Inequalities. 9.2 Polynomial and Rational Inequalities. 9.3 Absolute Value Equations. 9.4 Absolute Value Inequalities .. Using a Graph to Solve a Quadratic Inequality. Use the graph of in Figure 9-3 to solve the inequalities. a. b. x2. 6x. 8 7 0 x2. 6x. 8 6 0 f1x2 x2. 6x. 8. Example 1 ax2 bx c 6 0.
So, (1, 0) is a solution of the inequality. Shade the region inside the parabola. 3. 2. 1. EXAMPLE 1 quadratic inequalities in two variables. GOAL 1. Graph quadratic inequalities in two variables. Solve quadratic inequalities in one variable, as applied in Example 7. ? To solve real-life problems, such as finding the weight of
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