Characteristics of Quadratic functions

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Presentation transcript:

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

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

Average Rate of Change The average range of change between any two points (x1,f(x1)) and (x2,f(x2)) is the slope of the line through the 2 points.

Example 1 Find the average rate of change of f(x) = 2x2 – 3 when x1= 2 and x2 = 4.