Babylonian Mathematics

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

Square root method 𝑥 2 =16 𝑥−1 2 =4

Factoring 𝑥 2 +4𝑥+3=0 𝑥 2 −6𝑥+2=9

Moving on to Completing the Square… http://www.wisc-online.com/objects/ViewObject.aspx?ID=TMH1902

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

The Quadratic Formula 𝑥 2 −7𝑥+1=0

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

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

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

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: http://mathriddles.williams.edu/?p=107 )

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

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.

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

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