Graphing & Solving Quadratic Inequalities 5.7 What is different in the graphing process of an equality and an inequality? How can you check the x-intercepts of a quadratic equation or inequality? Why is it important to test 3 intervals after you have found the critical x values?

There are four types of quadratic inequalities in two variables. y < ax 2 + bx + c y ≤ ax 2 + bx + c y > ax 2 + bx + c y ≥ ax 2 + bx + c

Graphing a Quadratic Inequality in Two Variables 1. Draw the parabola. (Find vertex coordinates x=b/2a and substitute into the equation to find y. Then find one more point to draw the parabola.) Make the parabola dashed for inequalities with and solid for inequalities with≤ or ≥. 2. Choose a point (x,y) inside the parabola and check whether the point is a solution of the inequality. 3. If the point form step 2 is a solution, shade the region inside the parabola. If it is not a solution, shade the region outside of the parabola.

y > x 2 − 2x − 3 x = − b / 2a = y =

Graphing a System of Quadratic Inequalities y ≥ x 2 −4 y< −x 2 −x +2 x = − b / 2a = y= x=− b / 2a = y=

Solving a Quadratic Inequality by Graphing (Looking for x intercepts) x 2 − 6x + 5 < 0. Let y = 0 and factor to solve. (x−1)(x−5) = 0 x = 1 or x = 5 Solution 1<x<5

Solving a Quadratic Inequality by Graphing 2x 2 + 3x− 3 ≥ 0 (Use quadratic formula to factor.) 0.69 or −2.19

Solving a Quadratic Inequality Algebraically x 2 + 2x ≤ 8 x 2 + 2x − 8 =0 (x+4)(x−2)=0 x=−4 or x=2 012−1−2−3−4 Test x = −5 in the equation Test x = 0 in the equation Test x = 3 in the equation Solution is −4 ≤ x ≤ 2

What is different in the graphing process of an equality and an inequality? If the equation is > or <, the parabola is dashed. Either the inside or the outside of the parabola is shaded. Pick a point not on the parabola and see if it makes a true statement. If true, shade where the point is located. If not, shade the other area.

What is different in the graphing process of an equality and an inequality? How can you check the x-intercepts of a quadratic equation or inequality? Why is it important to test 3 intervals after you have found the critical x values?

Assignment 5.7 Page 303, 14-16, odd, skip 27, 39.