Characteristics of Quadratic functions

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Presentation transcript:

Characteristics of Quadratic functions f(x)= ax2 + bx + c (standard form) f(x) = a (x – h)2 + k (vertex form)

Vocabulary Parabola: The ____ shaped graph of a quadratic function. Domain: The set of ___-values of a relation. Range: The set of ___-values of a relation. Axis of Symmetry: A _________ line that divides the graph of a function into mirror images. Vertex: The point on the parabola that lies on the axis of symmetry.

Vocabulary X-Intercept: The point(s) at which a parabola crosses the _ -axis. Y-Intercept: The point(s) at which a parabola crosses the ___-axis. Zero: A value k whereas f(k)=0. (The __-values of the x-intercepts.) Maximum: The highest ___-value. Minimum: The lowest ___-value. ***Max. and Min. do not include , or -

For Example x= -2 (-2, -1) (0, 3) -3, -1 None -1 Domain Range AOS Vertex (-2, -1) X-intercept(s) (-3,0) (-1,0) Y-intercept(s) (0, 3) Zero(s) -3, -1 Maximum None Minimum -1

Now you try Domain Range AOS Vertex X-intercept(s) Y-intercept(s) Zero(s) Maximum Minimum

One more Domain Range AOS Vertex X-intercept(s) Y-intercept(s) Zero(s) Maximum Minimum

Increasing and Decreasing: Graph To find where the graph is increasing and decreasing trace the graph with your finger from left to right. Specify x-values! If your finger is going up, the graph is increasing. If your finger is going down, the graph is decreasing.