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Parabola f(x)= a(xh) 2(3h)^2  h determines x axis  ( 2 negatives= positive)  If a is positive parabola is up or to the right  Vertex is at (h,k)  if a is negative opens left or down  (x3)^{2} 5 >  move to the right  If parenthesis is addition, move to the left 
Graph the functions. Plot at least 3..  Make a table for eqaution   pick points for x   Solve   graph answers   should be in the form of f(x)=b^{x} 
Graph the functions. plot at least.. (Rules)if b>1 its a exponential growth function  if 0<b<1 its a exponential decay function  if b>1 Domain = ( infinity, infinity)  if b>1 Range = (0,infinity)  if b>1The line y=0 is horizontal asympote  if b>1 Function passes through (0,1) 
Shifting Parabolasf(x) = ax^{2}+bx+c is a parabola  f(x)= x^{2}+k  f(x)= (xh)^{2}  a>0 opens up  is a vertical shift of f(x)=x^2  h>0 shifted right vice versa  a<0 opens down  k>0 shifted up vice versa 
Quadratic functions of the form
  x (possible extra terms here)= square root of bSteps: get it in the form of the equation by adding and subtracting different sides
Apply sqaure root and the plus or mins sign
Find the inverseChange f(x) to y  Switch x & y  Solve for y 
Don't forget about cross multiplying
Solve log equation.Convert to exponential form based off of note  Simplify 
2^{3}= 8 which is log 8 = 3
Solve using Substitution.Substitute the same terms with a letter  Solve for the letter ex: (x=2)  Replace the letter with what was in the equation  Solve 
Solve the inequality using the test point method
Logarithmslog 1=1  Only solve multiple logs if they have the same base  log b^{x} =x  log (xy) = log (x) + log (y)  b^{log sub bx} =x  log 1=0  log b=1 
power is what it's equal to
base is the sub
  f and g functionsreplace f and g perform operation in middle  Horizontal line test  (g ∘ f )(x) = g(f(x))  intersects more than once, not a function 
Graphing inverseLook at > or < sign, determines what part of parabolas are the answer  Find the inverse  plot parabola from solved equation "y=..."  Make a table of points 
Solve the equation b = cGet bases same by putting a power or square root or fraction  Cross out bases  Exponents become base  Solve equation 
Sometimes doesnt look like example, general it has 2 numbers raised to a power with an equal sign between
Solving a Polynomial InequalityThink of it as a Quadratic equation (< OR > as a = sign)  Solve equation  Plot answers  Pick numbers from each A,B,C  if equation is tue part of solution  if false not part of solution  find and write out solution set 
Solving a Polynomial Inequality EX

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