igcse maths - algebraic and graph - graph of functions (quadratic, cubic....)
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Great understanding :)TRANSCRIPT
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