Cambridge Additional Mathematics

Quadratics (Chapter 3) 91

a Copy and complete:

Number of cuts,n 0 1 2 3 4 5

Maximum number of pieces,Pn

b Complete the¢ 1 and¢ 2 rows. Hence determine a quadratic formula forPn.

c For a huge pizza with 12 cuts across it, find the maximum number of pieces which can result.

Consider the graphs of a quadratic function and a linear function on the same set of axes.

Notice that we could have:

cutting

( 2 points of intersection)

touching

( 1 point of intersection)

missing

(no points of intersection)

If the graphs meet, the coordinates of the points of intersection of the graphs can be found bysolving the

two equations simultaneously.

Example 24 Self Tutor

Find the coordinates of the points of intersection of the graphs with equations

y=x^2 ¡x¡ 18 and y=x¡ 3.

y=x^2 ¡x¡ 18 meets y=x¡ 3 where

x^2 ¡x¡18 =x¡ 3

) x^2 ¡ 2 x¡15 = 0 fRHS=0g

) (x¡5)(x+3)=0 ffactorisingg

) x=5or¡ 3

Substituting into y=x¡ 3 , when x=5, y=2and when x=¡ 3 , y=¡ 6.

) the graphs meet at(5,2)and(¡ 3 ,¡6).

EXERCISE 3F

1 Find the coordinates of the point(s) of intersection of:

a y=x^2 ¡ 2 x+8 and y=x+6 b f(x)=¡x^2 +3x+9and g(x)=2x¡ 3

c y=x^2 ¡ 4 x+3 and y=2x¡ 6 d f(x)=¡x^2 +4x¡ 7 and g(x)=5x¡ 4

F Where functions meet

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_03\091CamAdd_03.cdr Thursday, 3 April 2014 4:47:59 PM BRIAN