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Material Type: Notes; Class: Precalculus (Phys & Math); Subject: Mathematics; University: Georgia College & State University; Term: Unknown 1989;
Typology: Study notes
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MATH 1113 Precalculus 3.3 notes
A _______________________ is a function of the form: ______________________________ where a , b , and c are real numbers and a ≠ 0 (Why?). The domain of a quadratic function consists of __________________________.
Examples of quadratic functions:
Properties of the quadratic function:
The Vertex = _______________________________
Axis of symmetry : _________________________
Parabola opens up if a > 0; the vertex is a ___________________ point.
Parabola opens down if a < 0; the vertex is a ___________________ point. For the following quadratic functions, find x and y -intercepts, axis of symmetry, vertex, and finally graph the equation. Also, state the domain and range.
If you can’t factor a quadratic equation, then you will need the ____________________________
to find the ___________________. The formula is ________________________________
Example: Graph f ( x )= − 2 x^2 + 8 x − 1 by transformations by putting in in the form f ( x )= a ( x − h )^2 + k. To do this we must __________________________
Notes on completing the square
Now, we will continue with the example: Graph f ( x )= − 2 x^2 + 8 x − 1 by transformations.
Let’s complete the square on f ( x )= ax^2 + bx + c if f ( x ) = 0 to find the x -intercepts.
3.3 Assignment 1-10 ALL, 11-18ALL, 19, 21, (27-33ALL- COMPLETE THE SQUARE), 35-51, 53- 58ALL