3 quadratic functions 1

7/28/2019 3 Quadratic Functions 1

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QUADRATIC FUNCTIONS

PAPER 1

1. Given 5)1(3)(2+= xxf . Find the minimum or maximum value off(x). [2 marks]

Answer: ........

2. Diagram 1 shows the graph of a quadratic function2( ) 2y x k= , where k is a

constant.

DIAGRAM 1

Find

(a) the value of k,

(b) the equation of the axis of symmetry,

(c) the coordinates of the maximum point. [3 marks]

Answer: (a) ...

(b) ..

(c)

...

1

3

y

x0

(2, 3)


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3 Diagram 2 shows the graph of a quadratic function2( ) 3( ) 2f x x p= + + , where p is a

constant.

DIAGRAM 2

The curvey = f(x) has the minimum point (1, q), where q is a constant.

State

(a) the value of p,

(b) the value ofq,

(c) the equation of the axis of symmetry. [3 marks]

Answer: (a) p =

(b) q =

(c) .

4 Given that the graph of the quadratic function kxxxf ++= 8)( 2 touches the x-axis at

one point only. Find the value ofk. [3 marks]

Answer: ........

2

x

y

0

y = f(x)

(1, q)


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5 Given that the graph of the quadratic function pxxxf += 42)( 2 does not intersect the

x-axis. Find the range of the values ofp. [3 marks]

Answer: ........

6 Find the range of the values of p if the graph of the quadratic function12522)(

2++= ppxxxf intersects thex-axis at two different points. [4 marks]

Answer: ........

7 The straight line y = 5x 1 does not intersect the curve22y x x p= + + . Find the range

of the values ofp. [3 marks]

Answer: ........

3


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8 Find the range of the values ofx for 2 4 5 0x x > . [3 marks]

Answer: ........

9 Find the range of the valuesx forx(x 4) 12. [3 marks]

Answer: ........

10 Find the range of the values ofx for( 3)( 4) 6x x+ < . [3 marks]

Answer: ........

4


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11 Find the range of the values ofx for ( 3)(2 4) ( 3)( 3)x x x x + > + . [3 marks]

Answer: ........

12 Given that 3 4 12x y+ = , find the range of the values ofx ify< 6. [3 marks]

Answer: ........

13 Find the range of the values ofx if 6y 1 = 4x and 3y> 2 +x. [3 marks]

5


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Answer: ........

14 Diagram 3 shows the graph of a quadratic function ( )y f x= . The straight line 4y =

is a tangent to the curve ( )y f x= .

( )y f x=

DIAGRAM 3

(a) Write the equation of the axis of symmetry of the curve.(b) Express ( )f x in the form of

2( )x b c+ + , where b and c are constants. [3 marks]

Answer: (a)

(b) ...

15 Find the range of the values ofx for (2 1)( 4) 4x x x + > + . [2 marks]

Answer: ........

6

y

x0 1 5

y = 4


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PAPER 2

16 The function 154)( 22 ++= kkxxxf has a minimum value of r2 + 2k, where rand k

are constants.

(a) By using the method of completing the square, show that r= k 1. [4 marks]

(b) Hence, or otherwise, find the values of k and r if the graph of the function is

symmetrical aboutx = r2 1. [4 marks]

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Answer

PAPER 1

1. Minimum value = 5

2. (a) k= 1

(b) x = 1

(c) Maximum point (1, 2)

3. (a) p = 1

(b) q = 2

(c) Axis of symmetryx = 1

4. k= 165. p> 2

6. p< 4, p> 6

7. p> 1

8. x 5

9. 2 x 6

10. 2 4

13. x >2

3

14. (a) x = 3

(b) 4)3( 2 = xy

15. 4x < or 1x >

PAPER 2

16. r= 3, k= 4

r= 1, k= 0

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3 quadratic functions 1

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