Section 7.2
Graphing Quadratic Functions
in Standard From
Method 2: Graphing by Using the Vertex Formula to Find the Vertex
Ve r t e x F o r m u l a
Process
To find the vertex of the graph of a quadratic
2
f
x
=
ax
+ bx + c
(
)
function
1. Find the x-coordinate of the vertex by using the
b
vertex formula x = − ,
2a
2. Find the y-coordinate of the vertex by evaluating f
at the value found in step 1.
b 

That is, find
f  − .
 2a 
−
Section 7.2
Lehmann, Intermediate Algebra, 4ed
Slide 2
Method 2: Graphing by Using the Vertex Formula to Find the Vertex
U s i n g t h e Ve r t e x F o r m u l a t o F i n d t h e Ve r t e x
Example
2
g
x
=
x
− 4 x + 7.
(
)
Find the vertex of the graph of
Solution
• a = 1, b = –4, and c = 7
• Find the x-coordinate by substituting a and b into
b
x= − :
the formula
2a
• Find the y-coordinate by finding f (2):
• So, the vertex is (2, 3)
Section 7.2
Lehmann, Intermediate Algebra, 4ed
Slide 3
Method 2: Graphing by Using the Vertex Formula to Find the Vertex
U s i n g t h e Ve r t e x F o r m u l a t o G r a p h a Q u a d r a t i c F u n c t i o n
Example
2
f
x
=
2
x
+ 10 x + 7.
(
)
Sketch a graph of
Solution
• a = 2, b = 10, and c = 7
• Find the x-coordinate of the vertex:
• Find the y-coordinate of the vertex:
• So, the vertex is (–2.5, –5.5)
• Find additional input-output pairs:
Section 7.2
Lehmann, Intermediate Algebra, 4ed
Slide 4
Method 2: Graphing by Using the Vertex Formula to Find the Vertex
U s i n g t h e Ve r t e x F o r m u l a t o G r a p h a Q u a d r a t i c F u n c t i o n
Solution
Example
Continued
Section 7.2
Lehmann, Intermediate Algebra, 4ed
Slide 5
Method 2: Graphing by Using the Vertex Formula to Find the Vertex
U s i n g t h e Ve r t e x F o r m u l a t o G r a p h a Q u a d r a t i c F u n c t i o n
Example
2
f
x
=
−
2.2
x
+ 6.1x + 1.4.
(
)
Sketch a graph of
Solution
• a = –2.2, b = 6.1, and c = 1.4
• Find the x-coordinate of the vertex:
• Find the y-coordinate of the vertex:
• So, the vertex is (1.39, 5.63)
• Find additional input-output pairs:
Section 7.2
Lehmann, Intermediate Algebra, 4ed
Slide 6
Method 2: Graphing by Using the Vertex Formula to Find the Vertex
U s i n g t h e Ve r t e x F o r m u l a t o G r a p h a Q u a d r a t i c F u n c t i o n
Solution
Example
Continued
Section 7.2
Lehmann, Intermediate Algebra, 4ed
Slide 7
Minimum of Maximum Value
M a x i m u m o f M i n i m u m Va l u e o f a F u n c t i o n
Property
2
f
x
=
ax
+ bx + c whose
(
)
For a quadratic function
graph has vertex (h, k),
• If a < 0, then the parabola opens downward and the
maximum value of the function is k
• If a > 0, then the parabola opens upward and the
minimum value of the function is k
Section 7.2
Lehmann, Intermediate Algebra, 4ed
Slide 8