Algebra 2 Notes (9-4)
Graphs of Quadratic Functions
Words to Know
• parabola• quadratic function• vertex of a parabola-
Words to Know
• parabola- graph of a quadratic function
• quadratic function- a function whose
equation is in the form of _____________
f(x)  ax2  bx  c
0
where a____
• vertex of a parabola- the point where the
graph crosses the line of symmetry
2
Graphs of f(x)  ax
• Vertex of graphs will always be (0, 0)
• Line of symmetry will always be on the yx0
axis which means ____
• Example 1
2
f(x)

2x
– Graph the equation
– What is the line of symmetry?
– What is the vertex?
Example 1 Solution
• The line of symmetry is ____
x0
(0, 0)
• The vertex is ____
• The graph of the function is:
line of
symmetry
vertex (0, 0)
2
Graphs of f(x)  a(x  h)
• Vertex of graphs will always be (h, 0),
where h can be any real number
• Line of symmetry will be x  h
• Example 2
2
– Graph the equation f(x)  (x  2)
– What is the line of symmetry?
– What is the vertex?
– What is the shift of the graph from the
equation f(x)  x2? (Shifting will be more indepth in Chapter 9-5)
Example 2 Solution
• The line of symmetry is ____
x2
(2, 0)
• The vertex is ____
• The graph of the function is:
line of
symmetry
vertex (2, 0)
Example 2 Solution (cont.)
• The shift of the graph from the origin is
two units to the right.
_________________
f(x)  x 2
f(x)  (x  2) 2
2
Distinguishing Between f(x)  (x  h)
2
• If the equation of the graph is f(x)  (x  h) , then
the following statements are true.
– The line of symmetry will be x  h
– The vertex will be (h, 0)
– The graph will always move to the left.
2
f(x)

(x

h)
• If the equation of the graph is
, then
the following statements are true.
– The line of symmetry will be x  h
– The vertex will be (h, 0)
– The graph will always move to the right.
Homework
• Pg.402 #1-25
– For the first 4 problems you don’t need to
graph, just determine whether it is above or
below the x-axis
– For problems #19-24, test out a point and see
where the inequality makes sense.