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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,

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**The graph of a quadratic equation is a PARABOLA.**

MM2A3c c. 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.

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**MM2A3c c. Investigate and explain characteristics of quadratic functions**

y x Parent Quadratic Function: f(x) = x2 Let’s graph it with a table of values!! x f(x) Now let’s describe it!!

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**The lowest or highest point on a parabola **

MM2A3c c. 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)

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**The set of all input (x) values of a relation **

MM2A3c c. 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

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**The set of all output (y) values of a relation **

MM2A3c c. 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

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**Interval(s) of Increase: From left to right on a graph, **

MM2A3c c. 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

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**Interval(s) of Decrease: From left to right on a graph, **

MM2A3c c. 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

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**Let’s practice 1 more MM2A3c c**

Let’s practice 1 more MM2A3c c. Investigate and explain characteristics of quadratic functions

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

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

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

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MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals.

MM2A3c Investigate and explain characteristics of quadratic function, including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, intervals.

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