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.

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Presentation transcript:

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,

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.

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!!

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)

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

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

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

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

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

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

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

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