1. 3.3 Q UADRATIC E QUATIONS & I NEQUALITIES

2. Q UIZ Tell true or false of the following statement: given linear functions f(x) and g(x), if (fg)(x) = 0, then either f(x) = 0 or g(x) = 0.

3. Q UADRATIC E QUATIONS Solve quadratic equations by factoring Solve by square root method Solve by the quadratic formula.

4. Q UADRATIC E QUATION IN ONE VARIABLE Quadratic equation in standard form:

5. S OLVE BY F ACTORING 3y(y - 1) = 0 X 2 – 49 = 0 X 2 + 11x = 12 6p 2 – 5p = 6 2x 2 + 4x -16 = 0 X 2 -6x + 9 =0 Fact: Given two functions f(x) and g(x), if (fg)(x) = 0, then either f(x) = 0 or g(x) = 0. Fact: Given two functions f(x) and g(x), if (fg)(x) = 0, then either f(x) = 0 or g(x) = 0.

6. S QUARE ROOT METHOD x 2 = 49 (4x - 3) 2 = 36 (1 - z) 2 = 8 (a + 2) 2 = -5 Fact: Given a function f(x), if ( f(x) ) 2 = B, B ≥ 0, then f(x) = ± √ B. Fact: Given a function f(x), if ( f(x) ) 2 = B, B ≥ 0, then f(x) = ± √ B.

7. Q UADRATIC FORMULA x 2 + 5x + 7 = 0 3p 2 + 7p -2 = 0 (x - 3)(x + 5) = -7 The solutions of the quadratic equation ax 2 + bx + c = 0, where a ≠ 0, are given by the formula x = The solutions of the quadratic equation ax 2 + bx + c = 0, where a ≠ 0, are given by the formula x = - b ± √ b2 – 4ac 2a

8. D ISCRIMINANT b 2 – 4ac is called the discriminant of the quadratic equation Value of b 2 – 4acNumber of SolutionsType of Solutions PositiveTwoReal 0One(identical solution)Real NegativeTwoNonreal complex

9. D ISCRIMINANT AND G RAPH Value of b 2 – 4ac Number of Real Solutions No. of x-intercepts PositiveTwo 0One(identical solution)One NegativeNone

10. S OLVING Q UADRATIC I NEQUALITIES a > 0a < 0 xx If x 1 < x < x 2, then f(x) < 0 If x = x 1 or x 2, then f(x) = 0 If x x 2, then f(x)> 0 If x 1 0 If x = x 1 or x 2, then f(x) = 0 If x x 2, then f(x)< 0 x1x1 x1x1 x2x2 x2x2

11. S OLVING Q UADRATIC I NEQUALITIES 1. Solve the corresponding quadratic equation Finding the x- intercepts of the function 2. Identify the intervals determined by the solutions of the equation 3. Use a test value from each interval to determine which intervals from the solution set

12. S OLVING Q UADRATIC I NEQUALITIES x 2 + 4x -12 ≥ 0 x(x-7) < 8 x 2 + 4x +4 < 0 x 2 + 6x +9 > 0 2x 2 + 4x +4 < 0 -x 2 + 4x - 6 > 0

13. H OMEWORK PG. 189: 5 – 50(M5),51,55,60 PG. 190: 63,66,68, 72 – 93(M3), 95 – 103(odds) KEY: 30, 45, 51, 95 Reading: 3.4 Modeling Reminder: Project 2 Due March 2 nd Skill test 2 Due March 4 th Exam 2 March 7 th,8 th