1. Quadratics
Objective 1: Students will be able to identify and convert between different forms of quadratics.
Objective 2: Students will be able to solve for the vertex and zeros of a quadratic.
Objective 3: Students will be able to solve real world situations involving quadratics.

2. 3 Forms of a Quadratic
Up to a 3 term polynomial Degree 2 Variables just stand for numbers, except h and k will represent a specific point Each one has its benefits when working with them and finding different parts of the parabola Standard form Factored form Vertex form

3. Converting Between Some of these we have already discussed
Standard to Factored
We already worked on factoring trinomials
2. Factored to standard
We already talked about foiling
3. Vertex to Standard
1. FOIL or expand the binomial
2. Distribute a
3. Combine like terms
4. Standard to Vertex
Complete the square

4. Examples

5. Completing the Square when a=1
Write terms in order
Group 1st 2 terms
(b/2)^2
Add value from step 3 inside the ( ) and subtract outside
Trinomial inside the ( ) is a perfect square trinomial, factor it
Combine like terms outside the ( )

6. Example

7. Vertex
Vertex is the min or max point of the parabola, where it changes directions, how we described the movement of the graph Vertex form easiest – think of the movement of the graph, that is the vertex (h,K) Standard is an equation to find the values Factored form you need to convert to standard

8. Examples

9. Roots and Zeros Roots and Zeros are really the same thing
You are trying to find where the graph crosses the x axis, so when y=0
Standard form – put in either factored form, vertex form, or use quadratic formula
2. Factored form – set each part equal to zero and solve
3. Vertex form – should be set equal to zero
Move k
Divide by a
Square root – remember to take both positive and negative
Move h

10. Examples

11. Word Problems Do they give you the formula
What do they want you to find
Max height or lowest point is the vertex
Starting point is the y intercept
Endpoint is the zeros

12. Example

13. Homework Worksheet on converting Worksheet on zeros and vertex
Worksheet on word problems