Quadratic equations functions

1.

The perimeter of this rectangular field is 220 m. One side is x m as shown.

Wm xm (a)

Express the width (W) in terms of x.

(b)

Write an expression, in terms of x only, for the area of the field.

(c)

If the length (x) is 70 m, find the area.

Working:

Answers:
(a) …………………………………………..
(b) …………………………………………..
(c) …………………………………………..
(Total 4 marks)

1

2.

The diagram shows the graph of y = x2 – 2x – 8. The graph crosses the x-axis at the point A, and has a vertex at B.

y

A

x

O

B
(a)

Factorize x2 – 2x – 8.

(b)

Write down the coordinates of each of these points
(i)

A;

(ii)

B.

Working:

Answers:
(a) …………………………………………..
(b) (i) ……………………………………..
(ii) ……………………………………..
(Total 4 marks)

2

3.

The diagram below shows a path x m wide around a rectangular lawn which measures 10 m by
8 m. xm 8m

LAWN

xm

10 m

(a)

Write down an expression in terms of x for the area of the path.

(b)

What is the width of the path when its area is 208 m2?

Working:

Answers:
(a) …………………………………………..
(b) …………………………………………..
(Total 4 marks)

4.

The perimeter of a rectangle is 24 metres.
(a)

The table shows some of the possible dimensions of the rectangle.
Find the values of a, b, c, d and e.
Length (m)

Width (m)

Area (m2)

1

11

11

a

10

b

3

c

27

4

d

e
(2)

3

(b)

If the length of the rectangle is x m, and the area is A m2, express A in terms of x only.
(1)

(c)

What are the length and width of the rectangle if the area is to be a maximum?
(3)
(Total 6 marks)

5.

(a)

Solve the equation x2 – 5x + 6 = 0.

(b)

Find the coordinates of the points where the graph of y = x2 – 5x + 6 intersects the x-axis.

Working:

Answers:
(a) …………………………………………..
(b) ..................................................................
(Total 4 marks)

4

6.

A picture is in the shape of a square of side 5 cm. It is surrounded by a wooden frame of width x cm, as shown in the diagram below.

5 cm x l

The length of the wooden frame is l cm, and the area of the wooden frame is A