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2026 Oxf Add Math Y10 Quadratic Functions _ Completed Square

Total questions: 46

Worksheet time: 1hrs 6mins

Name
Class
Date
1.

Write x2 + 4x + 10 in the form a(x+b)2 + c , where a, b and c are constants to be found

Working:

a=1, b= 42\frac{4}{2} , c=10, m=4

(x+m2)2 − (m2)2 +c\left(x+\frac{m}{2}\right)^2\ -\ \left(\frac{m}{2}\right)^2\ +c

=

2.

Find h for x2 + 4x + 10 in the form a(x-h)2 + k , where a, h and k are constants to be found.

Working:

From x2 + 4x + 10;

a=1, b=4, c=10

(x+b2)2 − (b2)2 +c\left(x+\frac{b}{2}\right)^2\ -\ \left(\frac{b}{2}\right)^2\ +c

=

3.

How to find the vertex (h ,k) of ax2+bx+c ?

Choose 2 options

a)

b)

c)

not sure!

d)

How!

4.

Write -2x2-4x+6 in the form z(x+ t)2 + c , where z, t and c are constants to be found.

Factorise -2x2-4x+6

Fill up the values of the two boxes

(a)  

5.

Write -2x2-4x+6 in the form z(x+ t)2 + c , where z, t and c are constants to be found.

-2(x+ ?)2 - ?2 -3

Fill up the values of the two boxes

(a)  

6.

Write -2x2-4x+6 in the form z(x+ t)2 + c , where z, t and c are constants to be found.

Fill up the values of the empty box

(a)  

7.

Write -2x2-4x+6 in the form z(x+ t)2 + c , where z, t and c are constants to be found.

Fill up the value of the box, for the expansion

Note: Is it negative or positive?

(a)  

8.

Write -2x2-4x+6 in the form z(x+ t)2 + c , where z, t and c are constants to be found.

Fill up the values of the two boxes

(a)  

9.

Write -2x2-4x+6 in the form z(x+ t)2 + c , where z, t and c are constants to be found.

Fill up the values of the two boxes

a)-2 1 8
b)-2
c)8
d)1
1
2
3
1)
2)
3)
10.

Write 2x2 + 4x -9 in the form a(x+b)2 + c , where a, b and c are constants to be found.

11.

Write -2x2-4x+6 in the form z(x+ t)2 + c , where z, t and c are constants to be found.

12.

Write 5x2-14x+8 in the form a(x+b)2 + c , where a, b and c are constants to be found.

13.

Hence write down the coordinates of the stationary point on the curve y=5x2-14x+8

*Using 5(x−75)2−955\left(x-\frac{7}{5}\right)^2-\frac{9}{5}

14.

Write -2x2-5x-4 in the form a(x+b)2 + c , where a, b and c are constants to be found.

15.

Hence write down the coordinates of the stationary point on the curve y=-2x2-5x-4

*Using −2(x+54)2−78-2\left(x+\frac{5}{4}\right)^2-\frac{7}{8}

16.

On the axes below, sketch the graph of y=|5x2-14x+8|,

stating the coordinates of the points where the graph meets the coordinate axes.

17.

Write down the range of values of z for which the equation |5x2-14x+8|=z has 4 distinct roots.

18.

Write the following quadratic expression in completed square form...

x2 - 4x - 2

19.

Write the following quadratic expression in completed square form...


x2 + 8x + 2

a)

(x + 4)2 - 14

b)

(x + 4)2 - 6

c)

(x + 4)2 - 18

d)

(x + 4)2 + 6

20.

Write the following quadratic expression in completed square form...


x2 + 8x - 1

a)

(x + 4)2 - 17

b)

(x + 4)2 - 16

c)

(x + 4)2 - 9

d)

(x + 4)2 - 15

21.

Write the following quadratic expression in completed square form...


2x2 + 20x + 26

a)

2(x + 5)2 -24

b)

(x + 5)2 + 3

c)

2(x + 5)2 + 12

d)

2(x + 5)2 - 25

22.

Write the following quadratic expression in completed square form...


x2 + 10x + 23

a)

(x + 5)2 - 2

b)

(x + 5)2 + 2

c)

(x + 5)2 + 13

d)

(x + 5)2 - 13

23.

Write the following quadratic expression in completed square form...


-3x2 - 30x - 4

a)

-3(x + 5)2 +71

b)

(x + 5)2 - 71

c)

2(x + 5)2 -71

d)

5(x + 5)2 - 13

24.

Write the following quadratic expression in completed square form...


x2 - 10x - 4

a)

(x - 5)2 - 29

b)

(x - 5)2 - 21

c)

(x + 5)2 + 14

d)

(x + 5)2 - 29

25.

Write the following quadratic expression in completed square form...


x2 - 10x + 18

a)

(x - 5)2 + 7

b)

(x - 5)2 - 7

c)

(x + 5)2 + 7

d)

(x + 5)2 - 7

26.

Write the following quadratic expression in completed square form...


x2 - 2x + 5

a)

(x - 1)2 + 4

b)

(x - 1)2 - 4

c)

(x - 1)2 + 3

d)

(x - 1)2 + 7

27.

Write the following quadratic expression in completed square form...


x2 - 2x - 3

a)

(x - 1)2 + 4

b)

(x - 1)2 - 4

c)

(x - 1)2 - 2

d)

(x - 1)2 + 5

28.

Write the following quadratic expression in completed square form...


x2 - 6x - 3

a)

(x - 3)2 - 12

b)

(x - 3)2 - 6

c)

(x - 3)2 + 6

d)

(x - 3)2 + 3

29.

Write the following quadratic expression in completed square form...


x2 - 6x + 10

a)

(x - 3)2 - 1

b)

(x - 3)2 - 19

c)

(x - 3)2 + 1

d)

(x - 3)2 + 4

30.

Write the following quadratic expression in completed square form...


x2 - 6x + 4

a)

(x - 3)2 - 5

b)

(x - 3)2 - 13

c)

(x - 3)2 + 5

d)

(x - 3)2 + 4

31.

Write the following quadratic expression in completed square form...


x2 - 6x + 2

a)

(x - 3)2 - 7

b)

(x - 3)2 - 11

c)

(x - 3)2 + 11

d)

(x - 3)2 - 4

32.

How to find the vertex (h ,k) of ax2+bx+c ?

a)

b)

c)

not sure!

d)

How!

33.

Write the following quadratic expression in completed square form...


x2 - 12x + 25

a)

(x - 6)2 + 13

b)

(x - 6)2 - 11

c)

(x - 6)2 + 11

d)

(x + 6)2 - 13

34.

Write the following quadratic expression in completed square form...


x2 - 12x + 38

a)

(x - 6)2 + 2

b)

(x - 6)2 - 2

c)

(x - 6)2 + 24

d)

(x + 6)2 + 24

35.

Write the following quadratic expression in completed square form...


x2 + 20x + 88

a)

(x + 10)2 + 12

b)

(x - 10)2 - 12

c)

(x - 10)2 + 12

d)

(x + 10)2 - 12

36.

Write the following quadratic expression in completed square form...


x2 - 20x + 104

a)

(x + 10)2 + 4

b)

(x - 10)2 - 4

c)

(x - 10)2 + 4

d)

(x + 10)2 - 4

37.

Write the following quadratic expression in completed square form...


x2 - 14x + 36

a)

(x + 7)2 + 13

b)

(x - 7)2 - 13

c)

(x - 7)2 + 13

d)

(x + 7)2 - 13

38.

Write the following quadratic expression in completed square form...


x2 + 14x + 50

a)

(x + 7)2 + 1

b)

(x - 7)2 - 1

c)

(x - 7)2 + 1

d)

(x + 7)2 - 1

39.

Find the minimum or maximum point of the graph x2-4x+8

a)

Min (-2,4)

b)

Min (2,4)

c)

Max (-2,4)

d)

Max (2,4)

40.

Find the minimum or maximum point of the graph x2+12x+4

a)

Max (-6,-32)

b)

Max (6,-32)

c)

Max (6,-32)

d)

Min (-6,-32)

41.

Find the minimum or maximum point of the graph -x2 - 4x + 1

a)

Min (-2,-5)

b)

Max (-2,-5)

c)

Max (-2,5)

d)

Min (2,-5)

42.

Identify the 'a' value: y = 16x2 -8x -24

a)

16

b)

8

c)

-8

d)

-24

43.
Is this a max or min?
a)
max
b)
min
c)
cannot be determined
44.
Is this a max or min?
a)
max
b)
min
c)
cannot be determined
45.

Find the line of symmetry of the graph

a)

x = -1

b)

x = -2

c)

x = -3

46.

What is the axis of symmetry for the following equation?
y=4x2-8x+9

(Note: Change to Conpleted Form to find )

a)
x=-8
b)
x=1
c)
x=-1
d)
x=2

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