Transcript 6.1 Graphing Quadratic Functions

6.1 Graphing Quadratic
Functions
Objectives:
1. Graph quadratic functions
2. Find and interpret the max and
min of a quadratic function
Vocabulary
Quadratic Function
• described by the equation of the following form:
f(x)=ax²+bx+c where a≠0
ax² is the quadratic term
bx is the linear term
c is the constant
• Graph is a parabola
• Parts:
– Axis of symmetry
– vertex
Graphing a Quadratic Function
• Plug in values for x to find y and plot them
f(x)=x²+3x-1
x
f(x)
-2 -3
-1 -3
0
-1
1
3
2
6
-3 -1
Finding Parts to graph
• Find axis of symmetry, y-intercept and vertex.
b
axis of symmetry: x  
2a
y-intercept: let x=0
vertex: Plug axis in for x to find y
• Choose points on both sides of the axis to plot.
This will ensure that your graph is as wide or as
narrow as it should be.
Example
Example: f(x)=x²-4x+2
4
x2
x
Axis:
2(1)
y-int: y=2
Vertex (2, ?)
f(x)=2²-4(2)+2
f(x)=4-8+2
f(x)=-2
Vertex: (2,-2)
Points: (3, ) (4, ) (0, ) (1, )
(3, -1) (4, 2) (0, 2) (1, -1)
Max and Min
Every parabola has a maximum and
minimum value. This occurs at the vertex.
If the parabola faces up, the vertex is a
minimum. If the parabola faces down, the
vertex is a maximum. The y-value is the
max or min.
Example
Find the axis of symmetry, y-intercept,
vertex, graph it and determine if the vertex
is a max or min. f(x)=x²-6x+14
Homework
p. 291
14-42 EOE