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Functions Quadratic Functions y = ax 2 Quadratics y = ax 2 +c Quadratic Functions Quadratic Functions www.mathsrevision.com Int 2 Quadratics y = a(x-b) 2 Quadratics y = a(x-b) 2 + c Factorised form y = (x-a)(x-b)

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Starter Starter 2          4 x +6 x Q 3 .  S olve  3 x  + 1 = 19 1. Factorise the f ollowing. 2. Round to 3 sig. f igures. (a) 47856 (b) 0. 065797 (c) 2. 05700 www.mathsrevision.com Int 2
Learning Intention Learning Intention Success Criteria Success Criteria 1. 1. Understand the term function. Understand the term function. 1. To explain the term function. 2. 2. Work out values for a given  Work out values for a given  function. function. www.mathsrevision.com Int 2 Functions Functions

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www.mathsrevision.com Int 2 Functions Functions A roll of carpet is 5m wide. It is solid in strips by the area. If the length of a strip is x m then the area.  A  square metres, is given by A = 5x.  A(x) =5x Example A(1) = 5 x 1 =5 A(2) = 5 x 2 =10 A(t) = 5 x t = 5t We say A is a function of x. We write : The value of A depends on the value of x.
www.mathsrevision.com Int 2 Functions Functions Using the formula for the function we can make a table and draw a graph using  as the y coordinate. x x 0 0 1 1 2 2 3 3 4 4 5 5 A A 0 0 5 5 10 10 15 15 20 20 25 25 0 5 10 15 2 0 2 5 3 0 0 2 4 6 x y = A(x) In the case The graph is a  straight line We can this a Linear function.

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www.mathsrevision.com Int 2 Functions Functions For the following functions write down the gradient  and were the function crosses the y-axis f(x) = 2x - 1 f(x) = 0.5x + 7 f(x) = -3x Sketch the following functions. f(x) = x  f(x) = 2x + 7 f(x) = x +1
Now try MIA Ex 1 Ch14 (page 216) www.mathsrevision.com Int 2 Functions Functions

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Starter Starter www.mathsrevision.com Int 2         Cac ulat e  f (-1)  , f (0 )  and  f (2 ) Q 3 .  S olve  6 x  +1 = 5 5 2 1. Given the f unction f (x) = x 2. Round to 2 decimal places (a) 47.856 (b) 0.065797 (c) 2. 05500
Learning Intention Learning Intention Success Criteria Success Criteria 1. 1. To know the properties of a  To know the properties of a  quadratic function. quadratic function. 1. To explain the main properties of  the basic quadratic function y = ax 2      using graphical methods. 2. 2. Understand the links between  Understand the links between  graphs of  the form y = x graphs of  the form y = x 2   and    and  y =  y =  ax ax 2   www.mathsrevision.com Int 2 Quadratic Functions Quadratic Functions

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www.mathsrevision.com Int 2 Quadratic Functions Quadratic Functions A function of the form  f(x) = a x 2  + b x + c is called a quadratic function  a, b  and  c   ar e  c o ns t ant s a 0 The simplest quadratics have the form f(x) = a x 2 Lets investigate
Now try MIA Ex 2 Q2 P 219 www.mathsrevision.com Int 2 Quadratic Functions Quadratic Functions

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