Precalculus - Section 3.3 Notes | MATH 1113, Study notes of Pre-Calculus

Material Type: Notes; Class: Precalculus (Phys & Math); Subject: Mathematics; University: Georgia College & State University; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 08/03/2009

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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.
1. xxxf 23)( 2=
pf3
pf4
pf5

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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.

  1. f ( x )= 3 x^2 − 2 x
  1. f ( x )=− x^2 + 4 x
  2. f ( x )= x^2 − 4 x + 3
  3. f ( x )= 2 x^2 + 9 x + 7

If you can’t factor a quadratic equation, then you will need the ____________________________

to find the ___________________. The formula is ________________________________

  1. f ( x )= x^2 − 7 x + 1

Example: Graph f ( x )= − 2 x^2 + 8 x − 1 by transformations by putting in in the form f ( x )= a ( xh )^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