Exam Questions Quadratics an Funtions (1)

8/11/2019 Exam Questions Quadratics an Funtions (1)

1/5

1. The diagram represents the graph of the function

f:x (xp)(x q).

x

y

C

21

2

(a) Write down the values ofpand q.

(b) The function has a minimum value at the point C. Find thexcoordinate of C.

(Total 4 marks)

2. The e!uationx2 2kx" 1 # $ has two distinct real roots. Find the set of all possible values of k.

(Total 6 marks)

3. (a) %&pressf (x)= x2 'x" 1 in the formf (x) # (xh)

2" k where h and kare to be

determined.

(b) *ence or otherwise write down the coordinates of the verte& of the parabola with

e!uationyx2 'x " 1.

(Total 4 marks)

4. (a) %&press + # 2x2 12x" 2, in the formy# 2(x c)

2" d.

The graph ofy#x2is transformed into the graph ofy# 2x

2 12x" 2, b+ the transformations

a vertical stretch with scale factor kfollowed by

a hori-ontal translation ofpunits followed by

a vertical translation of qunits.

(b) Write down the value of

(i) k

(ii) p

(iii) q.(Total 6 marks)

1


2/5

2


3/5

5. The diagram shows part of the graph ofy= a (x h)2+ k. The graph has its vertex at P,

and passes through the point A with coordinates (, !).

/

0

1 $ 1 x

y

2

1

(a) Write down the value of

(i) h

(ii) k.

(b) alculate the value of a.

(Total 6 marks)

6. The functionfis given b+f (x) #x2" x forx,.

(a) Writef (x) in the form (xa)

2

" b.

(b) Find the inverse functionf1

.

(c) 3tate the domain off1

.

(Total 6 marks)

7. Two functionsfg are defined as follows:

f:x ,x " 4g :x 2(1 x)

Find

(a) f1

(2)

(b) (g f )().

(Total 4 marks)

3


4/5

8. "et f (x) = 2x+ and g (x) = #x2 $.

Find

(a) f1

(x)

(b) (gf) (2)

(c) (fg) (x).

(Total 6 marks)

9. Three of the following diagrams 5 55 555 56 represent the graphs of

(a) y# , " cos 2x

(b) y# , cos (x" 2)

(c) y# 2 cosx" ,.

5dentif+ which diagram represents which graph.

x

1

2

1

2

3

2

y

2

1

1

2

x

1

2

1

2

3

2

y

,

2

1

,

y

x

(

2

1

2

1

2

3

2

x

1

2

1

2

3

2

4

(

,

2

1

y

5

5 5 5

5 5

5 6

(Total 4 marks)

4


5/5

10. 7etf(x) # ,(x" 1)2 12.

(a) 3how thatf(x) # ,x2" 'x .

(2)

(b) For the graph off

(i) write down the coordinates of the verte&

(ii) write down the equationof the a&is of s+mmetr+

(iii) write down theyintercept

(iv) find bothxintercepts.()

(c) !en"es8etch the graph off.(2)

(d) 7etg(x) #x2. The graph offma+ be obtained from the graph ofgb+ the two

transformations:

a stretch of scale factor tin theydirection

followed b+

a translation of

.

q

p

Find

q

p

and the value of t.(3)

(Total 1# marks)

5

Exam Questions Quadratics an Funtions (1)

Documents

Transcript of Exam Questions Quadratics an Funtions (1)