Final Exam Algebra 2b

Simplifying Rational Exponents

(3x^2/3)^-3 --> 3^-3 (x^-2) --> 1/3^3x^2 --> 1/27x^2

Intro to Rational Exponents

(^3√x) ^2 = x^2/3 2=exponent 3=index

Inflection point

(h,k)

Solving with Rational Exponents and Radicals

Algebraic: Isolate the radical or rational exponent form Cancel out radical with its inverse power; Cancel out a rational exponent with its reciprocal power Solve for x Calculator: Y1= right side Y2= left side 2nd, Calc, 5, Enter 3x for intersection (x-value)

Solve Cubics by Grouping

Group the first two terms and then the last two terms Factor out the GCF for both sets Factor out the GCF one more time for both sets Use the zero product property to solve

Solving Cube Roots

Use PEMDAS Square root or Cube each side Then finish solving for the answer

Proving Inverses of Cubic and Cube Root Functions

When solved both equations should end up with x, that means they are true inverse of each other.

Solve Cubics using the Fundamentals of Algebra

Y1= and Y2= Use synthetic division Then Quadratic Formula, = answer

Solve Cubics by Graphing

Y= right side of equation Y= left side of equation Intersection(s) -> x-value= answer

Cubic Transformations F(x)= a(bx-h)^3 +k and F(x)= a^√bx-h +k

a: a<0 reflection across the x axis 0<a<1 compressed by a a>1 stretched by a b: b<0 reflection across the y axis 0<b<1 stretched by 1/b b>1 compressed by 1/b h: h<0 shift left h>0 shift right (if both b and h are present solve bx-h=0 for correct h value) k: k<0 shit down k>0shift up

Solve Cubics Using Sum/Difference of Cubes

a^3 + b^3 = (a + b) (a^2 - ab + b^2) a^3 - b^3 = (a - b) (a^2 + ab + b^2) To Solve x^3 + 27=0 First Formula (positive equation) Use the Zero Product Property Use the Quadratic Formula then you have the answer

Cubic and Cube Root Functions

y = x^3 inverse: y = ^3√x D and R: All Real Numbers 180º Rotational Symmetry