1. Solving Quadratic Functions
Lesson 5.5b

2. Finding Zeros
Often with quadratic functions     f(x) = a*x2 + bx + c   we speak of “finding the zeros”
This means we wish to find all possible values of x for which    a*x2 + bx + c = 0

3. Finding Zeros
Another way to say this is that we are seeking the x-axis intercepts
This is shown on the graph below
Here we see two zeros – what other possibilities exist?

4. Factoring Given the function x2 - 2x - 8 = 0
 Factor the left side of the equation    (x - 4)(x + 2) = 0
We know that if the product of two numbers   a * b = 0     then either ...
a = 0     or
b = 0
Thus either
x - 4 = 0    ==> x = 4     or
x + 2 = 0    ==> x = -2

5. Warning!!
Problem ... many (most) quadratic functions are NOT easily factored!! 
 Example:

6. Completing the Square
We work with a quadratic equation to make one side a perfect square
Then we take the square root of both sides
Not forgetting to use both the + and - values of the right side of the equation

7. The Quadratic Formula
 We can use completing the square with the general  equation
ax2 + bx + c = 0.
Once this is done, we can use the formula for any quadratic function.

8. The Quadratic Formula
 It is possible to create two functions on your calculator to use the quadratic formula.
quad1 (a,b,c)           which uses the    -b + ...
quad2 (a,b,c)           which uses the    -b - ...

9. The Quadratic Formula Try it for the quadratic functions
4x2 - 7x + 3 = 0                          
6x2 - 2x + 5 = 0

10. The Quadratic Formula
4x2 - 7x + 3 = 0  

11. The Quadratic Formula
Why does the second function give "non-real result?“
6x2 - 2x + 5 = 0

12. Assignment
Lesson 5.5b
Page 220
Exercises 27 – 35 odd