modul 3 fungsi kuadratik.doc

7/21/2019 MODUL 3 FUNGSI KUADRATIK.doc

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MODUL SOLAF MATEMATIK TAMBAHAN 2014

MODUL 3 / TG4: FUNGSI KUADRATIK

KERTAS 1

1. Diberi f!"#i $%&r%'i$ ()3*2 2 ++= xy . N+%'%$%!

Given the quadratic function ()3*2 2

++= xy . State

*%) $,,r&i!%' 'i'i$ -%$#i--

the coordinates of the maximum point

1 - / Ar%# R

*b) er#%-%%! %$#i #i-e'ri.

the equation of the axis of symmetry.

1 - / Ar%# R

2. R%% 2 -e!!$$%! "r%f f!"#i ()1* 2 ++= xy &e!"%! $e%&%%! mi%% e-%%r.

Le!"$!" i' -e!+e!' "%ri# my = &i 'i'i$A&%! -e!+i%!" %$#i5y&i 'i'i$B.

Le!"$!" i' "% -e!+i%!" %$#i5x&i 'i'i$P.

Diagram 2shows the graph of the function ()1* 2 ++= xy where m is a constant.

The curve touchesthe line my = at point A and cut the y-axis at point B. The curve

also cut the xaxis at point P.

R%% 2

Diagram2

*%) Te!'$%! !i%i m&%! !i%i !.

Determine the value of m and of !.

2 - / Ar%# S

*b) N+%'%$%! $,,r&i!%' b%"i 'i'i$P.

State the coordinates of point P.

2 - / Ar%# S

M351

Ox

y

y6 m

B*0 !)

A

P


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3. R%% 3 -e!!$$%! "r%f f!"#i $%&r%'i$ )*xfy = . G%ri# r# (=y i%%

'%!"e!

%&% e!"$!" )*xfy = .

Diagram 3shows the graph of a quadratic function )*xfy = . The straight line

(=y

is a tangent to the curve )*xfy = .

R%% 3

Diagram3

*%) Ti#$%! er#%-%%! %$#i #i-e'ri b%"i e!"$!" i'.

"rite the equation of the axis of symmetry of the curve#

1 - / Ar%# R

*b) U!"$%$%! )*xf &%%- be!'$ qpx ++ 2)* &e!"%! $e%&%%!p&%! q%&%%

e-%%r.

$xpress )*xf in the form of qpx ++ 2)* where p and q are constants.

2 - / Ar%# S

M352

)*xfy =

0 1 7

y

y6 (

x


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4. R%% 4 -e!!$$%! "r%f f!"#i $%&r%'i$ 4)*3)* 2 ++= pxxf &e!"%! $e%&%%!p

i%% e-%%r.

Diagram 4shows the graph of a quadratic function 4)*3)* 2 ++= pxxf where p is a

constant.

R%% 4

Diagram4

Le!"$!" )*xfy = -e-!+%i 'i'i$ -i!i-- *2 q)&e!"%! $e%&%%! q%&%%

e-%%r.

The curve )*xfy = has the minimum point *2 q)where q is a constant.

N+%'%$%!

State

*%) !i%ip

the value of p

1 - / Ar%# R*b) !i%i q

'e 8%e ,f q

1 - / Ar%# R

*9) er#%-%%! %$#i #i-e'ri.

the equation of the axis of symmetry.

1 - / Ar%# R

M353

yy 6f *x)

x*2 q)

%


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. F!"#i $%&r%'i$ qpxaxf ++= 2)*)* &e!"%! $e%&%%! ap&%! q%&%% e-%%r

-e-!+%i !i%i -i!i-- . ;er#%-%%! %$#i #i-e'ri i%%x6 3.

The quadratic function qpxaxf ++= 2)*)* where ap and q are constantshas a

maximum value of . The equation of the axis of symmetry is x & 3.

N+%'%$%!State

*%) %' !i%i a

the range of values of a

1 - / Ar%# R

*b) !i%ip

the value ofp

1 - / Ar%# R

*9) !i%i q'e 8%e ,f q.

1 - / Ar%# R


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The function 23)* x)xaxf = has a minimum value of * when x & 2. (ind the

value of a and of ). 3 - / Ar%# T

10. D%%- R%% 10 'i'i$ *2


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11. =%ri %' !i%ixb%"i .:):)*23* >+ xxx

(ind the range of values of x for which .:):)*23* >+ xxx

3 - / Ar%# S

12. =%ri %' !i%ixb%"i 12)* 2 ++= )xxxf #e!'i%#% ber%&% &i %'%# %$#i5x. =%ri

%' !i%i ).

M357


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Given that the graph of quadratic function >2)* 2 ++= )xxxf always lies a)ove the

x-axis# (ind the range of values of )#

3 - / Ar%# S

KERTAS 2

1. Diberi f!"#i $%&r%'i$ 231


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Given the quadratic function 231


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2 - / Ar%# S

*b) L%$%r$%! "r%f )*xf i' !'$ &,-%i! 24 x .

S!etch the graph of )*xf for domain 24 x .

2 - / Ar%# S*9) N+%'%$%! %' +%!" #e%&%! b%"if*).

State the range to )*xf .

1 - / Ar%# R

4. S%' f!"#i $%&r%'i$ 0)/*2)* 2 !hxxf += &e!"%! $e%&%%! h&%! !i%% e-%%r

-e-!+%i 'i'i$ -i!i--P*2t 3t2).

A quadratic function 0)/*2)* 2 !hxxf += where h and ! are constants' has a

minimum point P*2t 3t2).

*%) N+%'%$%! !i%i h&%! !i%i !&%%- #eb'%! t.

State the value of h and of ! in terms of t.

2 - / Ar%# R

*b) Ci$% t6 2 9%ri$%! %' !i%i n#%+% er#%-%%!f*x) 6 n -e-!+%i !9%5!9%

!+%'%.

+ft6 2find the range of n such that the equation fx. & n has real roots.

3 - / Ar%# T

. R%% -e!!$$%! e!"$!" b%"i f!"#i $%&r%'i$ qxpy += 2)1* . Ti'i$ *1 ()

i%% 'i'i$ -%$#i-- e!"$!" i'.

Diagramshows the curve of a quadratic function qxpy += 2)1* . The point *1 ()

is the maximum point for the curve.

M3510


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R%%

Diagram

=%ri$%!

(ind

*%) !i%i5!i%i q+%!" -!"$i! &%! !i%i5!i%ip+%!" #e%&%!

the values of p and the corresponding values of q

4 - / Ar%# T

*b) %i !i%iy&%%- &,-%i!


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modul 3 fungsi kuadratik.doc

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