igcse maths - algebraic and graph - graph of functions (quadratic, cubic....)

QUADRATIC GRAPH

Amiruddin bin Razale

Muhammad Iskandar Zulqarnain bin Mohd Ishak

Mohamad Daniel Hakeem bin Md Nazri

Muhammad Adam Qusyairi bin Zamzury

Wan Faris Haziq bin Wan Jalalludin

MEMBER OF THE

TEAM

Quadratic GraphThe general expression for a quadratic function that takes the form ax2 + bx +c where a, b and c are constant. Some examples of quadratic functions are given below.

If a graph of quadratic funtion is plotted, the smooth curve produced is called a parabola.

y = 2x2 + 3x – 12 y = x2 – 5x y = x2

parabola

REMEMBER ! THE SHAPE OF LINE OF QUADRATIC GRAPH MUST BE CURVE.

TABLE

VALUE

REPLACE VALUE

There are two ways that we can use to solve the quadratic graph of function :

1) First, look at the question given.

2) For example:

Using this equation, construct a table of values and plot a graph.

3) Construct a table value as the question need.

* using a table, we can find the coordinates.

Y = x2 + x – 2 -4 ≤ x ≤ 3

TABLE VALUE SOLVING

Y = x2 + x – 2 -4 ≤ x ≤ 3

AXIS X

WE’LL GET THE VALUE OF AXIS Y USING THE TABLE

Y = x2 + x – 2 -4 ≤ x ≤ 3

We’ll considered the red font (x,y) colour as the coordinate.

x -4 -3 -2 -1 0 1 2 3

X2 16 9 4 1 0 1 4 9

+x -4 -3 -2 -1 0 1 2 3

-2 -2 -2 -2 -2 -2 -2 -2 -2

Y = x2

+ x –

2

10 4 0 -2 -2 0 4 10

x y

-4 10

-3 4

-2 0

-1 -2

0 -2

1 0

2 4

3 10

-4 -3 -2 -1 1 2 3

10

8

6

2

4

-2

-4

-6

-8

-10

0

REPLACE VALUE SOLVING

1. Replace x value with the value

given.

e.g 1 :

2x2 – 1 -3≤ x ≤ 3

2x2 – 1 -3≤ x ≤ 3

Replace x one by one following the value -3≤ x ≤ 3

2x2 – 1 2(-3)2 – 1 17

2(-2)2 – 1 7

2(-1)2 – 1 1

2(0)2 – 1 -1

2(1)2 – 1 1

2(2)2 – 1 7

2(3)2 – 1 17

x y

-3 17

-2 7

-1 1

0 -1

1 1

2 7

3 17

-3 -2 -1 1 2 3

15

12

9

6

3

-3

0

EXERCISE