9.3 Graphing Quadratic Functions
Quadratic Functions
Quadratic functions are functions written in the form
Every quadratic function has a U-shaped graph called a parabola.
2y ax bx c
Axis of Symmetry
Vertex
y = ax2 +bx + c When a>0, the parabola opens up. The vertex is the minimum point.
Positive a = smiley face
If the leading coefficient is positive, the parabola opens up, like a U.
Axis of Symmetry
Vertex
y = ax2 +bx + c When a<0, the parabola opens down. The vertex is the maximum point.
Negative a = Sad Face
If the leading coefficient is negative, the parabola opens down, like an upside-down U.
Parabolas
The lowest/highest point on a parabola is called the vertex.
The axis of symmetry is the line that runs through the vertex and divides the parabola in two symmetric parts.
The x-coordinate of the vertex, and the equation of the axis of symmetry will be the line
x = -b
2a
2y ax bx c
GRAPHING QUADRATIC EQUATIONS Make a table
Plot points and connect dots to make a smooth curve.
2y ax bx c
X Y
Quadratic Functions will be in the form
y = ax2 + bx + c or f(x) = ax2 + bx + c
The graph of a Quadratic Function will be a parabola.
y = x2
Use the table with the given values for x to find f(x). Then graph the function
X Y
-2
-1
0
1
2
y = 2x2
y = -2x2
Graph each function, and compare them to the graph of y = x2
y = 5x2
y = ¼ x2
X Y
-2 20
-1 5
0 0
1 5
2 20
X Y
-8 16
-4 4
0 0
4 4
8 16
y = x2
y = 5x2
y = ¼ x2
Do you notice any patterns here?
As the coefficient (a) of x2 gets larger, the graph gets narrower;And if the coefficient is less than 1, the graph is wide.
Homework
Section 9.3Page 521, # 5-10, and # 11,12,14,15,19
Plus, Box and Whisker Question on Handout (See page 375)BONUS: Do p. 378, #8-10,#15-17