1. Standard Factored Vertex
3 Forms of Quadratics
Standard
Factored
Vertex

2. Standard
a,b,c represent numbers in the equation Be able to find the vertex from this equation Factor this equation Complete the Square Solve for x (find the zeros of the function)

3. Vertex
(h,k) represent the vertex we have discussed before You need to find h and k using a,b,c H=-b/2a K=f(-b/2a) (what does this mean) Take the value you calculated, substitute it into the equation and solve for f(x) or y

4. Example

5. Check for Understanding
Find the vertex for each function

6. Factor
Can the trinomial be factored If yes this gives you factored form – we will discuss solving this a little later, already discussed factoring trinomails Complete the square – this gives you vertex form

7. Complete the Square Group 1st 2 terms
Factor out a (divide both terms by a)
Take second term inside parenthesis divide by 2 and square it
Add value from step 3 inside the ( ), multiple value from step 3 by what you factored out in step 2 and subtract it outside the ( )
Factor the trinomial – this is a special case, perfect square and should always break down to (square root of first sign of second square root of third) squared
Combine terms on the outside
If you did everything correctly then the graphs should be the same

8. Example

9. Check for understanding

10. Zeros
Solve the equation for x that will make the answer 0 Where the graph crosses the x axis Quadratic formula You could have 0,1 or 2 answers depending on your graph

11. Example
Find the zeros of the given function using the quadratic formula
X= 1,3
X= 0.28, -1.78

12. Factored form
Made up of at least 2 polynomials When multiplied out will give you a quadratic equation (degree 2) Rewrite in standard form – multiply out Find the zeros means to set each of the factored parts equal to zero and solve This could give you 1 or 2 solutions

13. Vertex Form
We have discussed this before when we talked about transformations State the vertex (h,k) Find the zeros Rewrite in Standard form

14. Find Zeros Set equation equal to zero Move k to other side Divide by a
Square root both sides
This is where you will determine if there is 0,1 or 2 solutions
Move h

15. Rewrite to standard form
Expand the equation out
FOIL
Distribute a
Combine like terms

16. Each equation has its benefits and draw backs.
You will practice all of these ideas and when asked to find the zeros of the function you can use any method you are most comfortable with