Alg III 1.7 lesson
Section 1.7
Quadratic Functions and their Graphs
­Form is f(x) = ax2 + bx + c, a ≠ 0
­Graph satisfies y = ax2 + bx + c
­Graph is called a PARABOLA
x­intercepts
when y = 0
"real roots"
Labels/Terminology
y­intercepts
when x = 0
Vertex
Axis of Symmetry
A.O.S
a­value
Opening
Vertex
a > 0
UP
Minimum
a < 0
DOWN
Maximum
1
Alg III 1.7 lesson
Parent Graph: y = x2
y = 3x2
y = ½ x2
Note: The bigger a­value the more narrower the parabola
Number of Roots
2 real roots
2 imaginary roots
1 real root
b2 ­ 4ac > 0
b2 ­ 4ac < 0
b2 ­ 4ac = 0
2
Alg III 1.7 lesson
Example 1
Find the intercepts, A.O.S., and vertex of the parabola. Sketch the graph and label.
y = x2 ­ 4x ­ 5 x­intercepts
y­intercepts
AOS
Vertex
Example 2
Find the intercepts, A.O.S., and vertex of the parabola. Sketch the graph and label.
y = x2 ­ 2x ­ 5 x­intercepts
y­intercepts
AOS
Vertex
3
Alg III 1.7 lesson
Another Way To Graph: y = a(x ­ h)2 + k
Vertex:
A.O.S: (h, k)
x = h
Example 3
Graph and label.
y = x2 + 4x + 9
Vertex
AOS
y­intercepts
x­intercepts
Methods of Graphing Parabolas
Method #1:
AOS
and Vertex
(plug in x­value & solve for y­value)
Method #2:
Note:
y = a(x ­ h)2 + K
y = ax2 + bx + c
H mew rk
p41 #4, 6, like ex:1&2
Vertex (h, k)
AOS x = h
the y­intercept is always the c­value
11, & 12, 15­19 all
ex:3
your way
4