September 23, 2017 | Author: Hayati Aini Ahmad | Category: Quadratic Equation, Cartesian Coordinate System, Abstract Algebra, Physics & Mathematics, Mathematics

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Quadratic Function_2011 Form 4 TERENGGANU 2011 1.

Find the range of values of

if

[3 marks]

2.

Diagram 1 shows the graph of the function constants.

where

and

are

(a)

State the equation of the axis of symmetry.

(b)

Find the value of

3.

Find the range of values of

if

4.

Find the range of values of

for which

5.

The quadratic equation equal roots. Find the values of .

6.

Diagram 2 shows the graph of the function intersects the y-axis at 10 and has the maximum point

and of

.

[3 marks]

has two different roots.[3 marks] [3 marks] , where

is constant, has two [3 marks] . The curve . Find

y

(2, q)

10 

(a)

the equation of the axis of symmetry

(b)

the value of

(c)

the value of

[3 marks]

x

7.

It is given that the quadratic function (a)

,

By using completing the square, express , where

and

in the form of are constants.

[2 marks]

(b)

Find the maximum or minimum value of

(c)

Sketch the graph for

(d)

State the equation of the curve when the graph is reflected in the -axis.

Prepared by: Pn. Hayati Aini bt. Ahmad

[1 mark] for

6 February, 2012

[3 marks]

Page 1

Quadratic Function_2011 Form 4 SELANGOR 2011 8.

Diagram 3 shows the graph of a quadratic equation is a constant. The curve has the maximum point constant. State (a)

the value of

(b)

the value of

9.

Find the range of values of

10.

Diagram 4 shows the graph of a quadratic function

where

[2 marks]

for which

(a)

Express equation of

(b)

Find

(i)

the minimum point of

, where is a

[3 marks]

in general form

by using the

completing the square method (ii)

the range of values of

such that

has no real roots

[6 marks]

SBP 2011 11.

Find the range of values of

for which

12.

Diagram 5 shows the graph of a quadratic function for

[3 marks] . Find

(a)

the value of

(b)

the equation of the axis of symmetry

(c)

the coordinates of the minimum point [3 marks]

Prepared by: Pn. Hayati Aini bt. Ahmad

6 February, 2012

Page 2

Quadratic Function_2011 Form 4 SARAWAK 2011 13.

Diagram 6 shows the graph of function , where Given that the line is the tangent to the curve. Find

14.

Find the range of values of

15.

is a constant.

(a)

the value of

(b)

the value of

(c)

the equation of axis of symmetry

which satisfies

[3 marks]

[3 marks] .

(a)

By using completing the square method, express where and are constants.

(b)

State the minimum or maximum point

(c)

Sketch the graph of

in the form of [2 marks] [1 mark]

for

[3 marks]

SABAH 2011 16.

can be expressed in the form of are constants. Find the value of and of .

and

[3 marks] PERLIS 2011 17.

Diagram 7 shows the graph of quadratic function where is a constant. State

Prepared by: Pn. Hayati Aini bt. Ahmad

for 0

(a)

the value of

(b)

the equation of the axis of symmetry. [2 marks]

6 February, 2012

Page 3

The quadratic function a maximum point . State (a)

19.

where

the range of values of

Find the range of value of

(b)

if

and

the values of

are constants, has

and

and

[3 marks] [3 marks]

PERAK 2011 20.

Diagram 8 shows the graph of a quadratic function is a tangent to the curve . (a)

. The straight line

Write the equation of the axis of symmetry of the curve.

(b)

Express where

in the form of

,

and are constants.

21.

Find the range of values of

which satisfies

22.

Diagram 9 shows the curve of a quadratic function has a minimum point at and intersects the

[3 marks]

[3 marks] . The curve -axis at point .

(a)

State the coordinates of

(b)

By using the method of completing the square, find the value of

(c)

and of .

[1 mark]

[4 marks]

Determine the range of values of , if [3 marks]

PENANG 2011 23.

Given that the quadratic function -axis, find the range of values of .

does not intersect the [3 marks]

PAHANG 2011 24.

Find the range of values of

for which

Prepared by: Pn. Hayati Aini bt. Ahmad

6 February, 2012

[3 marks]

Page 4

Quadratic Function_2011 Form 4 N.SEMBILAN 2011 25.

and

can be expressed in the form of are constants. Find the value of and of . [3 marks]

26.

Find the range of values of

for which

[3 marks]

MRSM 2011 27.

28.

Diagram 10 shows the quadratic function graph and are constants. The graph passes through the origin and point maximum value of is 3 units.

Find the range of values of

(a)

State the value of

(b)

Find value of .

, where . The

and of . [4 marks]

for which

[3 marks]

MELAKA 2011 29.

It is given that the quadratic function (a)

Write the equation of the axis of symmetry

(b)

State the coordinates of the minimum point

(c)

Write the equations when the graph is reflected through y-axis.

30.

Find the range of values of

31.

Express

for which

[3 marks]

is defined by in the form of

[3 marks]

, where , where

and

is a constant. are constants. [2 marks]

(b)

Find (i)

the value of

if the maximum value of

is and [2 marks]

(ii)

the range of values of

if the graph of

does not meet the x-axis. [3 marks]

Prepared by: Pn. Hayati Aini bt. Ahmad

6 February, 2012

Page 5

Quadratic Function_2011 Form 4 KELANTAN 2011 32.

Find the range of values of

for which

[4 marks]

33.

Diagram 11 shows the graph of quadratic function and are constants. State

, where

(a)

the value of

(b)

the value of

(c)

the equation of axis of symmetry [3 marks]

KEDAH 2011 34.

Diagram 12 shows the graph of the function the minimum point . State

. The curve has

(a)

the value of

(b)

the value of

(c)

the equation of axis of symmetry [3 marks]

35.

Diagram 13 shows the curve of a quadratic function has a minimum point and intersects the

Q

-axis at point .

(a)

Find the value of

(b)

State the coordinates of

(c)

Determine the range of values of , if .

Prepared by: Pn. Hayati Aini bt. Ahmad

. The curve

6 February, 2012

and of

[4 marks] [1 mark]

[3 marks]

Page 6