### Parabola f(x)= a(x-h) 2(-3-h)^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** | (x-3)^{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)= (x-h)^{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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