1. Babylonian Mathematics

2. You will be able to… Solve quadratic equations by Factoring
Using the Square Root Method
Completing the Square
Using the Quadratic Formula

3. Square root method
𝑥 2 =16
𝑥−1 2 =4

4. Factoring
𝑥 2 +4𝑥+3=0
𝑥 2 −6𝑥+2=9

5. Moving on to Completing the Square…

6. The Quadratic Formula
−𝑏 ± 𝑏 2 −4𝑎𝑐 2𝑎
Where do we find a, b, and c?

7. The Quadratic Formula
𝑥 2 −7𝑥+1=0

8. Can you… Solve quadratic equations by Factoring
Using the Square Root Method
Completing the Square
Using the Quadratic Formula

9. YOU will be able to…
Graph the following functions: constant, identity, square, cube, square root, cube root, reciprocal, absolute value
Graph functions using vertical and horizontal shifts
Graph using compressions and stretches
Graph using reflections over the x and y axis

10. Can you…
Graph the following functions: constant, identity, square, cube, square root, cube root, reciprocal, absolute value
Graph functions using vertical and horizontal shifts
Graph using compressions and stretches
Graph using reflections over the x and y axis

11. Today’s Riddle…
Consider an army with 10 generals. One wants a security system such that any three of them can determine the code to launch nuclear missiles, but no two of them can. It is possible to devise such a system by using a quadratic polynomial, such as a x^2 + bx + c; to launch the missiles, one must input (a,b,c). One cannot just tell each general one of a, b, or c (as then it is possible that some subset of three generals won’t know a, b and c); however, if a general knows two of (a,b,c), then a set of two generals can launch the missiles! What information should be given to the generals so that any three can find (a,b,c) but no two can? What about the general situation with N generals and any M can launch (but no set of M-1) can? (Source: )

12. YOU will be able to… Graph quadratics using transformations
Identify the vertex and axis of symmetry
Graph using the vertex, axis and intercepts
Find the maximum and minimum values of quadratics
Find an equation of a quadratic given vertex and a point

13. Vertex Form
As we saw on Monday, by completing the square we can obtain the following vertex form:
𝑦=𝑎 𝑥−ℎ 2 +𝑘
Your task is to use this known fact to complete questions 3 and 4 on the student worksheet that was passed out.

14. Vertex and Axis of Symmetry
Vertex is the point:
(− 𝑏 2𝑎 , 𝑓 − 𝑏 2𝑎 )
Axis of symmetry is the line:
𝑥=− 𝑏 2𝑎

15. Can you… Graph quadratics using transformations
Identify the vertex and axis of symmetry
Graph using the vertex, axis and intercepts
Find the maximum and minimum values of quadratics
Find an equation of a quadratic given vertex and a point