UNIT 2: SOLVING EQUATIONS AND INEQUALITIES Final Exam Review

TOPICS TO COVER  Simplifying Radicals  Quadratic Formula  Graphing Inequalities  Solving Systems of Inequalities

SIMPLIFYING RADICALS  Simplifying Radicals is necessary in math in order to simplify your answer COMPLETELY  Steps to Follow:  Break down the number under the radical using a FACTOR TREE  CIRCLE any pairs of numbers  The numbers that have a PAIR can be taken out of the radical and put on the OUTSIDE  If there is more than one pair, MULTIPLY the numbers on the outside of the radical  Write what is left over without a pair UNDER the radical symbol

SIMPLIFYING RADICALS  Watch this video to view and example

SIMPLIFYING RADICALS

QUADRATIC FORMULA

 Watch this video to hear the song that goes with the formula to help you remember it!

QUADRATIC FORMULA  In this problem, what is a, b, and c? y = 4x 2 – 3x + 5 Answer: a = 4 b = -3 c = 5

QUADRATIC FORMULA  Now try this problem. Use the quadratic formula to solve for x y = 2x 2 – 7x + 6

GRAPHING INEQUALITIES  Inequalities:, or ≥  To graph an inequality:  Put the inequality into “y=“  Go to TABLE to find the points to graph  Type of line:  If, use a DOTTED line  If ≤ or ≥, use a SOLID line  Shading:  If < or ≤, shade BELOW the line  If > or ≥, shade ABOVE the line

GRAPHING INEQUALITIES  Graph this inequality y < x 2 + 5x + 6 Dotted Line Shading Below

SOLVING SYSTEMS OF INEQUALITIES  Solving systems of inequalities allows you to find the MANY possible solutions to BOTH problems  Follow these steps:  Graph both inequalities in “y=“  Use the TABLE to graph both inequalities on your graph  Use the correct line and shade on the correct side of the line according to the sign  The answer to the system is where BOTH inequalities are shaded

SOLVING SYSTEMS OF INEQUALITIES  Watch this video for an example:

SOLVING SYSTEMS OF INEQUALITIES  Now try this one: y > 2x 2 – 6 y ≤ -x 2 – x

ALL DONE