2-7 Solving quadratic inequalities Chapter 2 2-7 Solving quadratic inequalities

Objectives Solve quadratic inequalities by using tables and graphs. Solve quadratic inequalities by using algebra.

Solving quadratic inequalities Many business profits can be modeled by quadratic functions. To ensure that the profit is above a certain level, financial planners may need to graph and solve quadratic inequalities. A quadratic inequality in two variables can be written in one of the following forms, where a, b, and c are real numbers and a ≠ 0. Its solution set is a set of ordered pairs (x, y).

Solving quadratic inequalities A quadratic inequality in two variables can be written in one of the following forms, where a, b, and c are real numbers and a ≠ 0. Its solution set is a set of ordered pairs (x, y). y < ax2 + bx + c y > ax2 + bx + c y ≤ ax2 + bx + c y ≥ ax2 + bx + c

Solving inequalties

Example#1 Graphing Quadratic Inequalities in Two Variables Graph y ≥ 2x2 – 5x – 2 . Step 1 Graph the boundary of the related parabola y = 2x2 – 5x – 2 with a solid curve. Its y-intercept is –2, its vertex is (1.3, –5.1), and its x-intercepts are –0.4 and 2.9.

Example#1 continue Step 2 Shade above the parabola because the solution consists of y-values greater than those on the parabola for corresponding x-values.

Example#2 Graph each inequality. y < –3x2 – 6x – 7

Example#3 Solve the inequality by using tables or graphs. x2 + 8x + 20 ≥ 5

Example#4 Solve the inequality x2 – 10x + 18 ≤ –3 by using algebra.

Example#5 Solve the inequality by using algebra. x2 – 6x + 10 ≥ 2

Example#6 Solve the inequality by using algebra. –2x2 + 3x + 7 < 2

Student guided practice Let’s work on graphing quadratic inequalities worksheet problems 1-5 Do problems 24-26 on book page 115

Homework Do evens problems from 35-46 from the book page 115.

Closure Today we learn how to solve quadratic inequalities by graphing and by solving algebraically Next class we are going to continue with 2-9 operations with complex numbers/

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