1. ALGEBRA I : SECTION 9-1 (Quadratic Graphs and Their Properties)
11/20/2018
ALGEBRA I @
SECTION 9-1 : QUADRATIC GRAPHS and THEIR PROPERTIES

2. QUADRATIC FUNCTION : An equation of the form y = ax2 + bx + c
QUADRATIC FUNCTION : An equation of the form y = ax2 + bx + c. This is called STANDARD FORM.
Graph y = x2 – 4x + 1 x y -1 1 2 3 4 5
What is the domain and range?

3. 2) What is the name of the graph for #1?
Parabola is the name (shape) of the graph for a quadratic function.
3) What is the name of the maximum or the minimum point of a parabola?
Vertex
4) What are the coordinates for the vertex for the graph of #1?
(2, -3)

4. The equation for #1 was y = x2 – 4x + 1
The equation for #1 was y = x2 – 4x We can find the vertex without guessing by using the formula
y = (2)2 – 4(2) + 1
= 4 – 8 + 1
= -3
5) How do you find the y-coordinate?
Just “plug in” 2 for x in the original equation.
Therefore, the vertex is at (2, -3)

5. AXIS OF SYMMETRY : The vertical line that contains the vertex and splits the parabola into symmetric parts. The
equation is of the form A parabola is
symmetric about the axis of symmetry.
You can use the axis of symmetry to determine additional points on the parabola.
In order to graph a parabola, find the coordinates of the vertex, find the coordinates of a second point, and use the axis of symmetry to plot a third point.
Y-INTERCEPT : The point(s) where a graph crosses the y-axis. You can find the y-intercept by setting x = 0.

6. For each parabola : find the coordinates of the vertex, find the equation of the axis of symmetry, find the y-intercept, use the axis of symmetry to find a third point, and graph the parabola.
6) y = -3x2
How can we tell if the parabola opens up or down?
Look at the coefficient of x2 :
a < 0 : down
a > 0 : up
What is the domain and range?

7. What does the “+2” at the end of the equation do to the graph?
7) y = -3x2 + 2
What does the “+2” at the end of the equation do to the graph?
It shifts the graph up 2 units.

8. 8) Given y = ax2 + c, what are the effects of “a” and “c: on the graph?
Graphing calculator time!!!!

9. ALGEBRA I : SECTION 9-1 (Quadratic Graphs and Their Properties)
11/20/2018 a
a > 0 graph opens up
a < 0 graph opens down
The larger a is, the narrower the graph (stretched)
The smaller a is, the broader the graph (compressed) c
+ c The graph shifts up c units
- c The graph shifts down c units

10. Examples of parabolas in everyday life.