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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