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 __________. | |

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| |2. f(x) = x2 + 9 + 8x |

| |Find the y-intercept = the eq. of the ax.|

| |Of sym.= the x-coor. of|

| |the vert.= |

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| |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 | |

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|b2 -4ac > 0; b2 -4ac is not pef.sq. | |

|2 real, irrational roots | |

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|b2 -4ac = 0 | |

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|1 real, rational root | |

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|b2 -4ac < 0 | |

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|2 complex roots | |

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|Solving Quadratic Functions | |

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|Method | |

|Can be Used | |

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|Graphing | |

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|Factoring | |

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|Square Root Property | |

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|Completing the Square | |

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|Quadratic Formula | |

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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 |

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|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. | |

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| |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. | |

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| |Solve by graphing: |

| |2. x2 + 2x – 3 > 0 |

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| |3. 0 > 3x2 -7x -1 |

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| |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? |

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|Solve Quadratic Inequalities | |

|To solve a _____________ ________________in one variable, use the graph of the related | |

|quadratic function | |

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|Solve a quadratic inequality algebraically, Ex: x2+x>6 | |

|Solve the related quadratic equation. | |

|Plot the solutions on a number line, using open circles: | |

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|Test a value in each section to see if it satisfies the original inequality. | |

|Write the answer as a solution set. | |

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