1. Graphing Quadratic Functions
Lesson 5-1 Part 3

2. MAIN IDEAS
How to determine if the function has a Minimum or a Maximum value
State the maximum of minimum value of the function
State the domain and range of the function

3. MINIMUM OR MAXIMUM For the graph of f(x) = ax2 + bx + c where a ≠ 0
When a > 0 the graph opens UP and has a MINIMUM
When a < 0 the graph opens DOWN and has a MAXIMUM

4. Example of MAXIMUM or MINIMUM
Consider the function f(x) = x2 – 6x + 8
Determine a, b, c → a= 1, b= -6, c= 8
Since a > 0, the graph opens UP and has a MINIMUM
For f(x) = - x2 + 2x + 3
Determine a, b, c → a= -1, b= 2, c= 3
Since a < 0 the graph opens DOWN and has a MAXIMUM

5. STATING THE VALUE OF THE MINIMUM OR MAXIMUM
The maximum/minimum value of the function is the y-coordinate of the vertex
For example in the function f(x) = x2 – 6x + 8 we determine the vertex by
finding the axis of symmetry,
plugging that value back into the function to find the y-coordinate
-b/2a = -(-6)/2(1) = 6/2 = 3
f(3) = (3)2 – 6(3) + 8 = -1; the y-coordinate of the vertex is -1
The value of the MINIMUM (since a>0) is -1

6. YOUR TURN TO THE FIND VALUE OF THE MINIMUM OR MAXIMUM
State the maximum or minimum value for the function f(x) = 2x2 + 5x + 3
Determine if the graph has a Minimum or Maximum
a=2; a>0 so it opens UP and has a MINIMUM
find the axis of symmetry, -b/2a
-(5)/2(2) = -5/4 = -1.25
- Plug that value back into the function to find the y-coordinate
f(-1.25) = 2(-1.25)2 +5(-1.25) + 3 = – =
the y-coordinate of the vertex is
The value of the MINIMUM is