FRONT OF CARD
|FRONT OF CARD |BACK OF CARD |
|Quadratic Function |General form: |
|General Form |[pic] |
|Vertex Form |Vertex form: |
| |[pic] |
|Graph Quadratic |Vertex [pic] |
| |[pic] |
| |[pic] |
| |Axis: [pic] |
| |Find point: |
| |narrow – one unit from vertex |
| |wide – more than one unit |
| |Label: vertex, axis, point |
|Find intercepts of quadratic fct |x-intercepts |
| |y=0, solve, ordered paris |
| |y-intercept |
| |f(0), ordered pair |
|Application: |y-value of vertex. |
|quadratic function |y-value is max/min |
|find max or min |x-value is where the max/min occurs (for example, at time t) |
|Graphs of polynomials are … |Smooth – no sharp points |
| |Continuous – no breaks |
|Definition of a zero of a function. |[pic] is a zero of function [pic] if [pic] |
|Equivalency Theorem |Given polynomial function [pic] |
| |[pic]is a zero of fct [pic] |
| |[pic] is an x-intercept on the graph of[pic] |
| |[pic] is a solution to [pic] |
| |[pic] is a factor of[pic] |
|Only change the sign when … |going to or from a factor. |
|End behavior – Leading Coefficient Test |[pic]both up |
|[pic] |[pic]both down |
| |[pic] left down, right up |
| |[pic] left up, right down |
|Multiplicities of zeros |even [pic]bounce |
| |odd [pic]through |
| |higher degree [pic] flatten |
|Intermediate Value Theorem (IVT) |If: |
| |[pic] is a polynomial function |
| |[pic] |
| |[pic]are opposite in sign |
| |Then: |
| |[pic] has at least one zero in [pic] |
|A polynomial function of degree n has … turning points |at most [pic] turning points |
|Graphing a polynomial |End behavior |
| |Zeros: |
| |x=zero |
| |multiplicity |
| |means … |
| |Find points as needed |
| |Draw graph |
| |Label |
|Rational zero theorem |[pic] |
| |factors of [pic]are possible rational zeros |
|Find all zeros of a polynomial fct |Graph - x-int |
| |Divide Synthetically |
| |Quadratic formula |
|Find all solutions to a polynomial equation |Graph - x-int |
| |Divide Synthetically |
| |Quadratic formula |
|Imaginary zeros always … |… come in conjugate pairs |
|A poly of degree n has … zeros |exactly n |
|Rational fct: find vertical asymptotes |Set the denominator equal to zero and solve |
|Rational fct: find horizontal asymptotes |deg num < deg denom [pic] [pic] |
|[pic] |deg num = deg denom [pic] [pic] |
| |deg num > deg denom [pic] no HA |
|Slant Asymptote |When the degree of the numerator is exactly one more than the |
| |degree of the denominator. |
| |1) Divide denominator into numerator |
| |2) Throw away the remainder |
| |3) SA is [pic]quotient |
| | |
|Graph Rational Function |1) Plot Intercepts |
| |2) Asymptotes |
| |3) Extra points |
| | |
| | |
|Solve polynomial inequalities graphically |1) If poly > 0, then choose intervals where the graph is above |
| |the x-axis. |
| |2) If poly < 0, then choose intervals where the graph is below |
| |the x-axis. |
| |3) [pic] use parenthesis |
| |[pic] use brackets |
|Solve polynomial inequalities algebraically |1) Write as equation and solve to find boundary points. |
| |2) Put boundary points on a number line and use test points from|
| |each interval in the original inequality. |
| |3) Include all “yes” intervals in the solution. |
|Solve rational inequalities algebraically |Same process as solving polynomial inequalities, except: |
| |1) When finding boundary points, include any undefined values |
| |(denom = 0) |
| |2) Can’t include in the solution any boundary points that are |
| |undefined. |
|Direct variation |[pic] |
|Inverse variation |[pic] |
|Joint variation |y varies as the product of two or more quantities: |
| |[pic] |
|Combined variation |y varies both directly and inversely |
| |[pic] |
|Solve a variation problem |1) Write variation model |
| |2) Plug in values and solve for constant k |
| |3) Re-write var model with value for k |
| |4) Plug in values and solve for y |
| | |
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