Interactive Study Guide for Students: Trigonometric Functions
Interactive Study Guide for Students
Chapter 6: Quadratic Functions and Inequalities Section 1: Graphing Q.F.’s
|Graph Quadratic Functions |Examples |
|A ______________ _____________ is described by an equation of the following form: |1.Graph f(x) = 2x2 – 8x + 9 by making a table |
|__________ term |of the values. |
|f(x) = ax2 + bx + c , where a≠0 |x |
| |2x2–8x+9 |
|__________ term ___________ term |f(x) |
|The graph of a quadratic function is called a __________. |(x,f(x)) |
|All parabolas have an _________ of __________. The point at which the axis of symmetry | |
|intersects the parabola is called the __________. |0 |
|Graph of a quadratic function f(x) = ax2+ bx +c(a≠0): | |
|The y-intercept is a(0)2 + b(0) + c or ___. | |
|The equation of the axis of symmetry is x = _______ | |
|The x-coordinate of the vertex is __________. | |
| |1 |
| | |
| | |
| | |
| | |
| |2 |
| | |
| | |
| | |
| | |
| |3 |
| | |
| | |
| | |
| | |
| |4 |
| | |
| | |
| | |
| | |
| | |
| |[pic] |
| |2. f(x) = x2 + 9 + 8x |
| |Find the y-intercept = the eq. of the ax.|
| |Of sym.= the x-coor. of|
| |the vert.= |
| | |
| | |
| | |
| | |
| |Make a table, including the vertex, and graph. |
| |3. f(x) = x2 – 4x + 9 |
|Maximum and Minimum Values | |
|The y-coordinate of the vertex of the quadratic function is the _______________ value or | |
|____________ value obtained by the function. | |
|Graph of a quadratic function f(x) = ax2+ bx +c(a≠0): | |
|Opens _____ and has a minimum value when a>0 | |
|Opens _____and has a maximum value when a 0; b2 -4ac is pef.sq. | |
|2 real, rational roots | |
| | |
| | |
|b2 -4ac > 0; b2 -4ac is not pef.sq. | |
|2 real, irrational roots | |
| | |
| | |
|b2 -4ac = 0 | |
| | |
|1 real, rational root | |
| | |
| | |
|b2 -4ac < 0 | |
| | |
|2 complex roots | |
| | |
| | |
|Solving Quadratic Functions | |
| | |
|Method | |
|Can be Used | |
| | |
|Graphing | |
| | |
| | |
|Factoring | |
| | |
| | |
|Square Root Property | |
| | |
| | |
|Completing the Square | |
| | |
| | |
|Quadratic Formula | |
| | |
| | |
Chapter 6: Quadratic Functions and Inequalities Section 6: Analyzing Graphs of Q.E.’s
|Analyze Quadratic Functions |Examples |
|A ________ of ________ is a group of graphs that displays one or more similar characteristics. |Analyze the function, then draw it’s graph.|
|How is the parent graph y=x2 similar to family graphs y=x2+ 2 and y=(x-3)2? |1. y = (x + 2)2 + 1 |
| | |
|Each function above can be written in the form y=__________________ where (_, _) is the vertex |y=a(x-h)2+k |
|of the parabola and x = ___ is the axis of symmetry. This is called the ___________ form. | |
|A the values of h and k change, the graph of y=a(x-h)2+k is the graph of y=x2 translated: |h and k |
||h| units _____ if h is negative or |h| units ______ if h is positive, and |k |
||k| units _____ if k is positive or |k| units _______ if k is negative. | |
| | |
| | |
| | |
| |h |
| |a |
| | |
| | |
| | |
| | |
| |2. y = x2 + 8x -5 |
| |3. y = -3x2 + 6x -1 |
| |4. vertex=(-1,4), passes through (2,1) |
|Write Quadratic Functions in Vertex Form | |
|Complete the _______ to write the function in vertex form. | |
Chapter 6: Quadratic Functions and Inequalities Section 7: Graphing and Solving Q.I.
|Graph Quadratic Inequalities |Examples |
|To graph a ____________ _____________ in two variables, use the same techniques used to graph |Graph. 1. y >|
|linear inequalities in two variable. |-x2 -6x -7 |
|Graph the quadratic equation. Decide if the parabola should be solid or dashed. | |
|Test a point (x,y) inside the parabola. Check to see if the point is a solution of the | |
|inequality. | |
|If the point is a solution, shade the region _______ the parabola. If not, shade the region | |
|_________ the parabola. | |
| | |
| |Solve by graphing: |
| |2. x2 + 2x – 3 > 0 |
| | |
| | |
| | |
| |3. 0 > 3x2 -7x -1 |
| | |
| | |
| | |
| |4. A punted football is the function |
| |H(x)=-4.9x2+20x+1. At what time is the |
| |ball within 5 meters from the ground? |
| | |
| | |
|Solve Quadratic Inequalities | |
|To solve a _____________ ________________in one variable, use the graph of the related | |
|quadratic function | |
| | |
| | |
| | |
|Solve a quadratic inequality algebraically, Ex: x2+x>6 | |
|Solve the related quadratic equation. | |
|Plot the solutions on a number line, using open circles: | |
| | |
|Test a value in each section to see if it satisfies the original inequality. | |
|Write the answer as a solution set. | |
................
................
In order to avoid copyright disputes, this page is only a partial summary.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related download
- unit 19 linear and quadratic inequalities in one variable
- chapter 2 functions equations and inequalities
- unit 3 quadratic equations and functions
- interactive study guide for students trigonometric functions
- worksheet 38 7
- quadratic equations
- solving quadratic equations by graphing
- name
- introduction to graphing quadratic equations
Related searches
- study guide for philosophy 101
- study guide for photosynthesis pdf
- study guide for sat
- study guide for fdny certificate of fitness
- study guide for driving test
- study guide for the book of john
- study guide for luke 1
- study guide for bls
- study guide for the act
- printable study guide for revelation
- study guide for microbiology
- ged study guide for math