What is the terminology we use to analyze a quadratic function?

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Presentation transcript:

What is the terminology we use to analyze a quadratic function? Standard: MM2A3.c.

What can you tell me about this graph?

Domain Range The x-values in the graph The y-values in the graph Independent variables What you put into the function The y-values in the graph Dependent variables What you get out of the function

What is the domain and range?

What is the domain and range?

What is the domain and range?

Vertex The minimum or maximum value of a quadratic function.

Axis of Symmetry The vertical line through the vertex on the graph of a quadratic function. Left side will EXACTLY mirror the right side. ALWAYS follows the form x=_____.

Extrema Maximums Minimums The highest point on the graph The lowest point on the graph

What are the maximum and minimum?

Zeros and Roots The points where the graph crosses the x-axis Called a zero, because if you plug in the x-value, you get out a zero

What are the zeros?

Intervals of Increase Intervals of Decrease 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.

Give the intervals of increase and decrease

Give the intervals of increase and decrease

Give the intervals of increase and decrease

Intercepts Where a function crosses an axis. If it crosses the x-axis, it’s an x-intercept and y=0. If it crosses the y-axis, it’s a y-intercept and x=0. Make sure you know which part of the ordered pair is the zero!

Rates of Change The average range of change between any two points is the slope of the line through the 2 points.

Find the average rate of change between x = -2 and x = 0

Analyze this graph domain, range, axis of symmetry, vertex, extrema, intervals of increase and decrease, zeros