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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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Determine the value of k for which the expression can be factored using a special product pattern: x 3 + 6x 2 + kx + 8 The “x” = x, and the “y” = 2.

Determine the value of k for which the expression can be factored using a special product pattern: x 3 + 6x 2 + kx + 8 The “x” = x, and the “y” = 2.

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