It is only by following your deepest instinct that you can lead a rich
life, and if you let your fear of consequence prevent you from following
your deepest instinct, then your life will be safe, expedient and thin.
Standard Form: Review
Standard Form of a Quadratic Equation:
f ( x)  ax 2  bx  c, where a  0
What if the b = 0?
1) The vertex is at (0, c)
f ( x)  ax 2  c
10
2) Make a table of values with x values
on each side of the axis of symmetry.
8
1 2
Ex1) Graph f ( x)  x  3.
2
4
6
2
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
4
6
8 10
You try one!
Ex2) Graph f ( x)  2 x 2  8.
10
8
6
4
2
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
4
6
8 10
Properties of Parabolas
•If a > 0, parabola opens up; if a < 0, parabola opens down
•Axis of symmetry is
x
•Vertex:   b , f   b  
 2a
b
2a
 2a  
•y-intercept at (0, c)
10
Ex3) Graph f ( x)   x  4 x  2.
2
8
6
4
2
-10 -8 -6 -4 -2
2
-2
-4
-6
-8
-10
4
6
8 10
Now try this!
1 2
Ex4) Graph f ( x)  x  2 x  3.
3
Direction it opens?
10
Axis of Symmetry?
8
6
4
Vertex?
2
-10 -8 -6 -4 -2
y-intercept?
2
-2
-4
-6
***What is the minimum?
-8
-10
4
6
8 10
Application
Ex5) The number of weekend get-away packages a hotel can
sell is modeled by –0.12p + 60, where p is the price of a getaway package. What price will maximize revenue? What is the
maximum revenue?
Relate: revenue equals price times number of get-away packages sold
HW: p. 248 #1, 4, 7, 12, 17, 20, 26-29
It is only by following your deepest instinct that you can lead a rich
life, and if you let your fear of consequence prevent you from following
your deepest instinct, then your life will be safe, expedient and thin.