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GRAPHS OF FUNCTIONS
Sketch a graph according to the functions
Example :
2. y = -3x + 6
c=6
If y = 0, -3x + 6 = 0
-3x = -6
x=2
Points are (0,
6), (2, 0)
y
1. y = 2x
c = 0,
If x = 1, y = 2 (1)
y=2
Points are (0, 0), (1, 2)
y
y = -3x + 6
y = 2x
X (1, 2)
0 X
X
6
x
X
0 2
x
3. y = -3x2
i) a < 0, (shape of the graph is
ii) When b = 0, c = 0
Symmetry axis : x = 0 (y-axis)
iii) Maximum point is (0, 0)
y
Maximum point
X
0
x
y = -3x2
4. y = 4x2 + 2
i) a > 0 ( shape of the graph
is
ii) When b = 0, c ≠ 0
Symmetry axis : x = 0 (y
axis)
or
When x = 0, y = 4(0)2 + 2
y=2
y
y = 4x2 + 2
iii) c = 2
iv) Minimum point is (0, 2)
X
2
0
Minimum point
x
5. y = x2 – x
i) a > 0, shape of the graph is
ii) c = 0
iii) When b ≠ 0 and c = 0
Find the intersect of x-axis :
y
b
(-1)
x = - / a, x = - / 1 = 1
y = x2 – x
or
When y = 0,
x (x – 1) = 0
x = 0, 1
x
0
x
1
x
6. y = x2 – 3x - 4
i) a > 0, shape of the graph is
ii) When b ≠ 0,
Symmetry axis : x = - b/2a
x = - (-3)/2(1) = 1.5
When x = 1.5, y = (1.5)2 – 3(1.5) – 4
y = - 6.25
Minimum point is (1.5, -6.25)
iii) c = -4
iv) Find the intersect of x :
When y = 0, (x + 1)(x – 4) = 0
x = -1, 4
y
x = 1.5
y = x2 – 3x - 4
x
-1X 0
-4 X
X4
x
(1.5, -6.25)
Minimum point
Exercise
1.
2.
3.
4.
y=x–3
y = x2 – 3x
y = 4 – x2
y = x2 – x – 6
Answer
1. y = x – 3
2. y = x2 – 3x
y
y
y=x–3
0
x
3
x
0
x
y = x2 – 3x
-3 x
x
3
x
3. y = 4 – x2
4. y = x2 – x – 6
y
y
4
x
-2
y = x2 – x – 3
x
0
x
2
x
-2
x
0
y = 4 – x2
-6 x
x
3
x
1. y = 3x
2. y = 3x – 6
y
y
x (1, 3)
0
y = 3x
x
y = 3x – 6
x
0
-6 x
x
2
x
3. y = 3x + 4
4. y = - 3x
y
y
y = 3x + 4
x
0
4x
-4/
x
3
0
y = -3x
x
x
x
(1, -3)
6. y = x2 + 5
5. y = -3x - 6
y
y
y = x2 + 5
y = -3x - 6
0
x
2
x
5x
-6x
0
x
7. y = 8x2 – 2
8. y = -3x2 + 6x
y
y
y = 8x2 – 2
0
x
-1/2
0
x1
/2
x
-2 x
y = -3x2 + 6x
x
x
2
x
10. y = x2 + 2x – 15
9. y = 1/2x2 – 3x
y
y
y=
1/
2
x2
y = x2 + 2x – 15
+6
x
-5
0
x
x
6
x x
3
0
x
x -15