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Exploring Quadratic Functions: Characteristics and Analysis

Analyze quadratic functions, understand domains, ranges, intervals of increase/decrease. Explore parent quadratic function and its properties such as vertex, domain, and range.

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Exploring Quadratic Functions: Characteristics and Analysis

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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, intervals of increase and decrease,

  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 Domain: The set of all input (x) values of a relation In our parent function example: Domain = all real numbers or

  6. 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

  7. 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

  8. 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

  9. Let’s practice 1 moreMM2A3cc. Investigate and explain characteristics of quadratic functions

  10. Domain:The set of all input (x) values of a relation

  11. Interval(s) of Increase:From left to right on a graph, where as x increases, f(x) increases

  12. Interval(s) of Decrease:From left to right on a graph, where as x increases, f(x) decreases

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