1. Advanced Algebra Notes
Section: 4.1: Graphing Quadratic Functions in Standard Form
A __________________ in standard form is written where a
The graph of a quadratic function is called a ____________, which is a ___________ figure.
The parent graph of any quadratic function is f(x) = x2.
The vertex of the parent function is _______ and the line of symmetry is _______. The vertex is the highest or lowest point on the graph of a parabola.
Remember what the a value in an absolute value function told us about the graph, it is the same for a quadratic function.
A mathematician came up with a formula from completing the square on the quadratic function
If you would complete the square, you would end up with the function
quadratic function
parabola
U-shaped
(0, 0)
X = 0

2. Graph of a Quadratic Function in Standard Form
The graph of a Quadratic Function ( ) has the following characteristics:
** The parabola opens up if ________ and opens down if _______.
** If the parabola opens up the y-coordinate of the vertex is a ______________.
** If the parabola opens down the y-coordinate of the vertex is a _______________.
** The parabola is wider (fatter) than the graph of if ________ and narrower if ________.
** The x-coordinate of the vertex is equal to the formula _________ .
** The axis of symmetry is the vertical line _____________.
a > 0
a < 0
minimum value
maximum value
|a| < 1
|a| > 1

3. a = 1 , opens up , base shape Vertex: (0, -3) L. O. S.: x = 0
Example1: Graph f(x) = x2 - 3.
a = 1 , opens up , base shape
Vertex: (0, -3)
L. O. S.: x = 0
Minimum Value: -3

4. a = -1 , opens down , base shape
Example 2: Graph
a = -1 , opens down , base shape
Each box = .5

5. Vertex: (2, -2) L. O. S. : x = 2 Minimum Value: -2 Example 3: Graph .
Example 3: Graph
a = 2 , opens up, narrower
Vertex: (2, -2)
L. O. S. : x = 2
Minimum Value: -2

6. Example 4: Graph
, opens up , wider