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The Gatsby Charitable Foundation 1

MEP: Demonstration Project Teacher Support Y9B, P17

Practice Book UNIT 17 Quadratic Functions

17.1 Quadratic Expressions1. (a), (b), (c) graphs

(d) y x y x= = +2 2 3

translation 03

y x y x= = 2 2 2

translation 02

2.

y

x

9

8

7

6

5

4

3

2

1

3 2 1 0 1 2 3

1

2

y = x 2 + 3

y = x 2

y = x 2 2

y

x

9

8

7

6

5

4

3

2

1

3 2 1 0 1 2 3

1

2

3

4

5

6

7

8

9

10

y = 9 x 2

y = 4 x 2

y = 1 x 2

y = x 2

y = 1 x 2

Answers



3.

4.

5. (a)(b) ( 2, 8), (2, 8)

17.1

y

x

10

8

6

4

2

3 2 1 0 1 2 3

1

y = 3 x 2y = 4 x2

y = 34

x2

y = x2

y

x

1

3 2 1 0 1 2 3

1

2

3

4

5

6

7

8

9

y = 14

x2

y = 12

x2

y = 34

x2

y = x 2 y

x

10

8

6

4

2

3 2 1 0 1 2 3

1

y = 2 x 2

y = x2 + 4

Answers



6. (a)

(b) y x y x= = +( )2 21 translation

10

y x y x= = +( )2 23 translation

30

y x y x= = ( )2 22 translation 20

(c)

7. (a) (b)

(c) (d)

17.1

y

x

10

8

6

4

2

3 2 1 0 1 2 34 45

y = x + 3( ) 2

y = x + 1( ) 2

y = x 2( ) 2

y

x

3

2

1

3 2 1 0 1

y = x + 1( ) 2 + 1

x

y

1 2 3 4

1

2

3

4

0

y = x 3( ) 2 + 2

x0 1

y

3

2

1

2 3y = x 2( ) 2 3

x

y

0

3

2

1

12345

y = x + 4( ) 2 3

y

x

6

4

2

3 2 1 0 1 2 34 456 5 6 7

y = x + 4( ) 2 y = x 3( ) 2 y = x 5( ) 2

Answers



17.1

3

y

x012 1

y = x 2 + 2 x

3

y

0124567

y = x 2 + 6 x

9

8. (a), (b)

Lowest point 12

14

, Lowest point ( , )1 1

Lowest point ( 2, 4)

Lowest point of y x b x= +2 is

b b2 4

2

, .

Lowest point ( 3, 9)

(c)

(d) b b2 4

2

,

x012 1

y = x 2 + x

0 x

y

1 2y = x 2 4 x

3 40 x

y

1 2

y = x 2 x

x

y

0 1 2 3 4 5 6 7

y = x 2 6 x

x3

y

x012 145

y = x 2 + 4 x

Answers



17.1

9. (a)

(b) (0, 1) (0, 2)(c) (0, c)(d) ( 1, 1) ( 1, 1)(e) ( 1, c a )

10. (a)

(b)

ba

ac ba2

44

2

,

11. (a) c is the y-intercept (or value of y when x = 0 ) and graph shows y = 10 when x = 0

(b) a = 130

; b = 2

y

x

2

1

3 2 1 0 1

1y = 2 x 2 + 4 x + 1

y

x

2

1

3 2 1 0 1

1

3

y = 3 x 2 + 6 x + 2

x

y

12345

y = 2 x 2 + 8 x 1

0

6

4

2

8

10

x

y

1 2 3 4

2

4

6

8

0

y = 3 x 2 9 x + 7

x

y

0

3

2

1

12345

4

5y = x2 + 5 x + 1

Answers



17.2

17.2 Quadratic Equations: Factorisation1. (a) 3 7x +( ) (b) 5 4x ( ) (c) x x ( )1

(d) x x +( )6 (e) x x2 1( ) (f) 4 2 5x x+( )(g) 2 2 15x x( ) (h) x x5 16+( ) (i) x x2 2 1+( )

2. (a) x x+( ) +( )1 3 (b) x x( ) ( )1 2 (c) x x( ) +( )7 2(d) x x( ) ( )20 1 (e) x x+( ) +( )5 7 (f) x ( )5 2(g) x x( ) ( )5 6 (h) x x( ) +( )9 7 (i) x x( ) ( )6 8

3. (a) 0, 4 (b) 0, 3 (c) 0, 7

(d) 0, 14

(e) 0, 73

(f) 0, 52

4. (a) 2, 6 (b) 4, 2 (c) 3, 2(d) 4, 1 (e) 3, 5 (f) 2, 9(g) 3, 9 (h) 3, 7 (i) 1, 17(j) 5, 12

5. (a) 0, 8 (b) 0, 43

(c) 5, 10(d) 7, 10 (e) 8, 7 (f) 3, 17

6. (a)

(b) Graph crosses x-axis at two points, which are the x-values that give y = 0 .

y

x

3

2

1

3 2 1 0 14 2

4

1

2

3

4

3

y = x 2 + 2 x 3

Answers



17.2

7. (a) (b) One

(c) x +( ) =1 02so x +( ) =1 0 x = 1

8.

Graph does not cross x-axis, so there are no x-values forwhich y = 0 .

9. (c) w = 2 5 or (d) cannot have width = 5 (e) 2 cm by 5 cm

10. 4 cm 3

11. y y= =5 or 1

17.3 Quadratic Equations: Completing the Square1. (a) x +( ) 3 92 (b) x +( ) 2 42 (c) x +( ) 4 162

(d) x ( ) 5 252 (e) x +( ) 3 5 12 252. . (f) x ( ) 2 5 6 252. .2. (a) x +( ) 3 82 (b) x ( ) 4 132 (c) x +( ) 5 372

(d) x +( ) 6 282 (e) x ( ) 2 32 (f) x ( ) 3 122(g) x +( ) 2 5 3 252. . (h) x +( ) 1 5 6 252. .(i) x +( ) 0 5 2 252. . (j) x ( ) +0 5 2 752. .

3. (a) 4, 2 (b) 3, 1 (c) 6, 2(d) 1, 4 (e) 3, 5 (f) 7, 4

4. (a) 3.45, 1.45 (b) 4.24, 0.24(c) 6.74, 0.74 (d) 0.10, 10.10(e) 2.30, 1.30 (f) 0.38, 2.62(g) 5.70, 0.70 (h) 4.19, 1.19

5. (a) x x +( ) =4 20 (b) 2.9 cm6. (a) x ( ) + =4 2 02 (b) x ( )4 2 cannot be negative

y

x012 1

1

2

y = x 2 + 2 x + 1

y

x012 1

1

2

y = x 2 + 2 x + 2

Answers



17.3

7. (a) x x2 5 2 0+ = ; 5.37, 0.37(b) x x2 2 3 0 + = ; no solutions(c) x x2 2 3 0+ = ; 3, 1(d) x x2 6 3 0 = ; 0.46, 6.46

8. (a) 20 (b) t t= =1 3 or 9. 310. 53.0 cm11. 4.44948974, 0.44948974

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