Chapter 2 2-7 Solving quadratic inequalities

Solve quadratic inequalities by using tables and graphs.

Solve quadratic inequalities by using algebra.

Objectives

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 quadratic inequalities

Solving inequalties

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

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.

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

Example#2

Solve the inequality by using tables or graphs.

x2 + 8x + 20 ≥ 5

Example#3

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

Example#4

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

Example#5

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

Example#6

Let’s work on graphing quadratic inequalities worksheet problems 1-5

Do problems 24-26 on book page 115

Student guided practice

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

Homework

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/

Closure

Have a nice day!!!!