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CPM Section 9.1 “The Quadratic Function”. The quadratic function can be written in one of two ways : Standard Form:_________________ Vertex Form: :_________________ “ a” may not equal zero because there will be no squared term then.
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The quadratic function can be written in one of two ways: Standard Form:_________________ Vertex Form: :_________________ “a” may not equal zero because there will be no squared term then The Vertex Form is the form most useful when graphing. Let’s try a few. The vertex is the turning point. This one is a minimum (2,1)
The graph of a quadratic function is always a ________________. The graph will open up if ___________________. The graph will open down if ____________________. parabola a>0 (positive) a<0 (negative)
The most important point on a parabola is the vertex. The vertex is the _______________ on a parabola that opens up and the _____________ on a parabola that opens down. From the three examples above, we see that the vertex of a parabola will have the coordinates (__,__) NOTE: The vertex is also the point where the function switches from increasing to decreasing or vice-versa. lowest point highest point -h k
The domain of a quadratic function is _________________ while the range is….. _________ if _________ _________ if _________ all real #’s
Example: Consider the function 1. Domain 2. Range 3. Does the Parabola open up/down? always It opens down because a is negative Since a<0
Max/Min? Vertex For what values of x is the function What is the value? Increasing and/or Decreasing? Where does it occur? (-4, -5) Increasing from The vertex is the (–h,k) Decreasing from The vertex is a maximum at (-4,-5)
Zero(s) ? 8. Graph Just set y=0 This tell you that the function will not cross the x-axis
