Chapter 1

Question	Answer
Properties of Equality	1. A=B if A+C=B+C 2. A=B if AC=BC when C=/=0
Solving Power Equations	-of the form x^n=a -has real solutions of x=n√a if n is odd x=+-n√a if n is even
Modeling With Equations	Strategy: 1. Identify variable 2. Translate words to algebra 3. Solve equations, check answer
Quadratic Equations	Is of the form ax^2+bx+c=0 where a, b, c include all real numbers
Solving Quadratics	1. Factoring 2. Complete the square 3. Quadratic formula
Quadratic Equation	x=(-b+-√b^2-4ac)/2a
The Discriminant	for ax^2+bx+c=0 -if D>0, equation has 2 real solutions -if D=0, equation has 1 real solution -if D<0, equation has no real solutions
i	i=√-1 i^2=-1 i^3=-i i^4=1
Square Roots of Negative Numbers	if -r is negative, its principal square root is √-r=i√r x^2=-r x=+-i√r
Properties of Inequalities	1. If A<B, then A+C<B+C 2. If A<B and C>0, then AC<BC 3. If A<B and C<0, then AC>BC 4. If A<B and A, B>0, then 1/A>1/B
Solving Nonlinear Inequalities	1. Move all terms to one side 2. Factor 3. Find intervals (values that make the expression=0) 4. Make table/graph using intervals 5. Test points in each interval
Properties of Absolute Values and Inequalities	1. \|x\|=c = x=+-c 2. \|x\|<c = -c<x<c 3. \|x\|>c = x>c or x<-c

Resource summary

	Created by Erin Mooney over 9 years ago