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MM2A3. Students will analyze quadratic functions in the forms f ( x ) = ax 2 + bx + c

Standard. MM2A3. Students will analyze quadratic functions in the forms f ( x ) = ax 2 + bx + c and f ( x ) = a ( x – h ) 2 + k .

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MM2A3. Students will analyze quadratic functions in the forms f ( x ) = ax 2 + bx + c

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  1. Standard MM2A3. Students will analyze quadratic functions in the forms f(x) = ax2 + bx + c and f(x) = a(x – h)2 + k. c. Investigate and explain characteristics of quadratic functions, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals of increase and decrease, and rates of change

  2. MM2A3cc. Investigate and explain characteristics of quadratic functions A quadratic function is a function that can be written in standard form: y = ax2 + bx + c where a is not equal to 0. The graph of a quadratic equation is a PARABOLA.

  3. y x MM2A3cc. Investigate and explain characteristics of quadratic functions Parent Quadratic Function: f(x) = x2 Let’s graph it with a table of values!! x f(x) Now let’s describe it!!

  4. MM2A3cc. Investigate and explain characteristics of quadratic functions Let’s define!! Vertex: The lowest or highest point on a parabola In our parent function example: Vertex: (0,0)

  5. MM2A3cc. Investigate and explain characteristics of quadratic functions Axis of Symmetry: An invisible vertical line that divides the parabola into mirror images and passes through the vertex. (x = ____) In our parent function example: Axis of Symmetry: x = 0

  6. MM2A3cc. Investigate and explain characteristics of quadratic functions Domain: The set of all input (x) values of a relation In our parent function example: Domain = all real numbers or

  7. MM2A3cc. Investigate and explain characteristics of quadratic functions Range: The set of all output (y) values of a relation In our parent function example: Range = or

  8. MM2A3cc. Investigate and explain characteristics of quadratic functions Zero(s): Where f(x) = 0; Where the graph of a function crosses or touches the x-axis In our parent function example: Zero: x = 0

  9. MM2A3cc. Investigate and explain characteristics of quadratic functions Extrema: The minimum(s) and maximum(s) of a function on a certain interval. The vertex’s y-coordinate is the: MINIMUM value if a>0 MAXIMUM value if a<0 In our parent function example: Extrema: Minimum at y = 0

  10. MM2A3cc. Investigate and explain characteristics of quadratic functions Interval(s) of Increase: From left to right on a graph, where as x increases, f(x) increases In our parent function example: Int. of Increase = x > 0 Or

  11. MM2A3cc. Investigate and explain characteristics of quadratic functions Interval(s) of Decrease: From left to right on a graph, where as x increases, f(x) decreases In our parent function example: Int. of Increase = x < 0 Or

  12. MM2A3cc. Investigate and explain characteristics of quadratic functions X-intercept(s): Point(s) where the function crosses or touches the x-axis In our parent function example: X-intercept: x = 0

  13. MM2A3cc. Investigate and explain characteristics of quadratic functions Y-intercept(s): Point(s) where the function crosses or touches the y-axis In our parent function example: y-intercept: y = 0

  14. MM2A3cc. Investigate and explain characteristics of quadratic functions Average Rate of Change: The slope of the line that passes through two given points on the function In our parent function example: On the interval: * Point 1 = (0,0) * Point 2 = (2,4) The average rate of change is 2

  15. Homework: Characteristics of Quadratic Functions Practice Sheet WRITE PROBLEMS and SHOW WORK for credit!!

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