EduSahara™ Assignment
Name : Graphical Representation of Quadratic Polynomial
Chapter : Polynomials
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Find the table of points that satisfy
the parabola equation
y
=
2
x
2
(i)
x
-2
-1
1
1
2
y
8
2
-1
2
8
(ii)
x
-2
-1
0
1
2
y
8
2
0
2
8
(iii)
x
-2
-1
0
1
4
y
8
2
0
2
10
(iv)
x
-2
-1
-2
1
2
y
8
2
-2
2
8
(v)
x
-2
-1
0
0
2
y
8
2
0
3
8
Question
2
2.
Find the table of points that satisfy
the parabola equation
y
=
(
−
2
x
2
)
(i)
x
-2
-1
0
1
4
y
-8
-2
0
-2
-6
(ii)
x
-2
-1
1
1
2
y
-8
-2
-1
-2
-8
(iii)
x
-2
-1
0
1
2
y
-8
-2
0
-2
-8
(iv)
x
-2
-1
-2
1
2
y
-8
-2
-2
-2
-8
(v)
x
-2
-1
0
0
2
y
-8
-2
0
-1
-8
Question
3
3.
Find the table of points that satisfy
the parabola equation
y
=
(
4
x
2
+
12
x
+
9
)
(i)
x
-2
-1
0
0
2
y
1
1
9
26
49
(ii)
x
-2
-1
0
1
4
y
1
1
9
25
51
(iii)
x
-2
-1
-2
1
2
y
1
1
7
25
49
(iv)
x
-2
-1
0
1
2
y
1
1
9
25
49
(v)
x
-2
-1
1
1
2
y
1
1
8
25
49
Question
4
4.
Find the table of points that satisfy
the parabola equation
y
=
(
−
x
2
−
4
x
−
3
)
(i)
x
-2
-1
0
1
2
y
1
0
-3
-8
-15
(ii)
x
-2
-1
1
1
2
y
1
0
-4
-8
-15
(iii)
x
-2
-1
0
1
4
y
1
0
-3
-8
-13
(iv)
x
-2
-1
-2
1
2
y
1
0
-5
-8
-15
(v)
x
-2
-1
0
0
2
y
1
0
-3
-7
-15
Question
5
5.
Find the table of points that satisfy
the parabola equation
y
=
2
x
2
(i)
x
-2
-1
0
0
2
y
8
2
0
3
8
(ii)
x
-2
-1
1
1
2
y
8
2
-1
2
8
(iii)
x
-2
-1
0
1
2
y
8
2
0
2
8
(iv)
x
-2
-1
-2
1
2
y
8
2
-2
2
8
(v)
x
-2
-1
0
1
4
y
8
2
0
2
10
Question
6
6.
Find the table of points that satisfy
the parabola equation
y
=
(
−
3
x
2
)
(i)
x
-2
-1
0
1
2
y
-12
-3
0
-3
-12
(ii)
x
-2
-1
0
1
4
y
-12
-3
0
-3
-10
(iii)
x
-2
-1
0
0
2
y
-12
-3
0
-2
-12
(iv)
x
-2
-1
1
1
2
y
-12
-3
-1
-3
-12
(v)
x
-2
-1
-2
1
2
y
-12
-3
-2
-3
-12
Question
7
7.
Find the table of points that satisfy
the parabola equation
x
=
y
2
(i)
x
4
1
1
4
y
-2
-1
1
2
(ii)
x
4
1
-2
1
4
y
-2
-1
-2
1
2
(iii)
x
4
1
0
1
6
y
-2
-1
0
1
4
(iv)
x
4
1
0
1
4
y
-2
-1
0
1
2
(v)
x
4
1
0
0
4
y
-2
-1
0
2
2
Question
8
8.
Find the table of points that satisfy
the parabola equation
x
=
(
−
4
y
2
)
(i)
x
-16
-4
0
-4
-14
y
-2
-1
0
1
4
(ii)
x
-16
-4
-2
-4
-16
y
-2
-1
-2
1
2
(iii)
x
-16
-4
0
-4
-16
y
-2
-1
0
1
2
(iv)
x
-16
-4
1
-4
-16
y
-2
-1
-1
1
2
(v)
x
-16
-4
0
-5
-16
y
-2
-1
0
2
2
Question
9
9.
Find the table of points that satisfy
the parabola equation
y
=
(
2
x
2
+
12
x
+
16
)
(i)
x
-2
-1
0
0
2
y
0
6
16
31
48
(ii)
x
-2
-1
1
1
2
y
0
6
15
30
48
(iii)
x
-2
-1
0
1
2
y
0
6
16
30
48
(iv)
x
-2
-1
0
1
4
y
0
6
16
30
50
(v)
x
-2
-1
-2
1
2
y
0
6
14
30
48
Question
10
10.
Find the table of points that satisfy
the parabola equation
x
=
(
2
y
2
+
8
y
+
8
)
(i)
x
0
2
8
18
32
y
-2
-1
0
1
2
(ii)
x
0
2
8
18
34
y
-2
-1
0
1
4
(iii)
x
0
2
6
18
32
y
-2
-1
-2
1
2
(iv)
x
0
2
8
17
32
y
-2
-1
0
2
2
(v)
x
0
2
9
18
32
y
-2
-1
-1
1
2
Question
11
11.
Find the table of points that satisfy
the parabola equation
y
=
(
3
x
2
−
6
x
−
9
)
(i)
x
-2
-1
1
1
2
y
15
0
-10
-12
-9
(ii)
x
-2
-1
0
1
2
y
15
0
-9
-12
-9
(iii)
x
-2
-1
0
0
2
y
15
0
-9
-11
-9
(iv)
x
-2
-1
0
1
4
y
15
0
-9
-12
-7
(v)
x
-2
-1
-2
1
2
y
15
0
-11
-12
-9
Question
12
12.
Find the table of points that satisfy
the parabola equation
x
=
(
−
4
y
2
−
8
y
−
3
)
(i)
x
-3
1
-5
-15
-35
y
-2
-1
-2
1
2
(ii)
x
-3
1
-3
-16
-35
y
-2
-1
0
2
2
(iii)
x
-3
1
-3
-15
-35
y
-2
-1
0
1
2
(iv)
x
-3
1
-2
-15
-35
y
-2
-1
-1
1
2
(v)
x
-3
1
-3
-15
-33
y
-2
-1
0
1
4
Question
13
13.
Find the roots of the quadratic equation
(
x
2
−
2
x
+
1
)
=
0
(i)
(
1
,
1
)
(ii)
no real roots
(iii)
(
4
,
1
)
(iv)
(
2
,
1
)
(v)
(
2
,
2
)
Question
14
14.
Find the roots of the quadratic equation
(
x
2
−
4
x
+
3
)
=
0
(i)
no real roots
(ii)
(
1
,
3
)
(iii)
(
2
,
3
)
(iv)
(
2
,
4
)
(v)
(
4
,
3
)
Question
15
15.
Find the roots of the quadratic equation
(
−
2
x
2
+
4
x
−
3
)
=
0
(i)
no real roots
(ii)
(
1
,
0
)
(iii)
(
4
,
0
)
(iv)
(
1
,
1
)
Question
16
16.
Which of the displayed parabolae represent
the equation
y
=
3
x
2
(i)
parabola with point
K
(ii)
parabola with point
M
(iii)
parabola with point
N
(iv)
parabola with point
L
Question
17
17.
Which of the displayed parabolae represent
the equation
y
=
(
x
2
+
4
x
+
3
)
(i)
parabola with point
C
(ii)
parabola with point
A
(iii)
parabola with point
B
(iv)
parabola with point
D
Question
18
18.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
36
16
4
0
4
16
36
(i)
y
=
4
x
2
(ii)
y
=
5
x
2
(iii)
y
=
7
x
2
(iv)
y
=
3
x
2
(v)
y
=
2
x
2
Question
19
19.
The given table of points satisfy which parabola equation?
x
9
4
1
0
1
4
9
y
-3
-2
-1
0
1
2
3
(i)
x
=
y
2
(ii)
x
=
0
(iii)
x
=
3
y
2
(iv)
x
=
(
−
2
y
2
)
(v)
x
=
2
y
2
Question
20
20.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
-54
-24
-6
0
-6
-24
-54
(i)
y
=
(
−
8
x
2
)
(ii)
y
=
(
−
5
x
2
)
(iii)
y
=
(
−
4
x
2
)
(iv)
y
=
(
−
7
x
2
)
(v)
y
=
(
−
6
x
2
)
Question
21
21.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
-2
0
4
10
18
28
40
(i)
y
=
(
x
2
+
5
x
+
10
)
(ii)
y
=
(
x
2
+
9
x
+
10
)
(iii)
y
=
(
2
x
2
+
7
x
+
10
)
(iv)
y
=
(
x
2
+
7
x
+
10
)
(v)
y
=
(
7
x
+
10
)
Question
22
22.
The given table of points satisfy which parabola equation?
x
-3
-2
-1
0
1
2
3
y
-15
-3
1
-3
-15
-35
-63
(i)
y
=
(
−
4
x
2
−
11
x
−
3
)
(ii)
y
=
(
−
4
x
2
−
5
x
−
3
)
(iii)
y
=
(
−
4
x
2
−
8
x
−
3
)
(iv)
y
=
(
−
5
x
2
−
8
x
−
3
)
(v)
y
=
(
−
3
x
2
−
8
x
−
3
)
Question
23
23.
Which of the displayed parabolae represents
the equation
y
=
3
2
x
2
(i)
parabola with point
M
(ii)
parabola with point
O
(iii)
parabola with point
L
(iv)
parabola with point
N
Question
24
24.
Which of the displayed parabolae represents
the equation
y
=
(
x
2
+
8
x
+
15
)
(i)
parabola with point
L
(ii)
parabola with point
O
(iii)
parabola with point
N
(iv)
parabola with point
M
Question
25
25.
Which of the following are true?
a)
The curve of a parabola
y
=
a
x
2
+
b
x
+
c
always croses the X-axis
b)
The curve of a parabola
is a
circle
c)
The curve of a parabola
is a
straight line
d)
The curve of a parabola
is a
curve
e)
The curve of a parabola
is a closed figure
f)
The curve of a parabola
lie in only one quadrant
(i)
{d}
(ii)
{f,d}
(iii)
{a,d}
(iv)
{c,e,d}
(v)
{b,d}
Question
26
26.
Which of the following are true for m > 0 and a > 0?
a)
The curve of a parabola
y
=
a
x
2
+
b
x
+
c
lies in the I & II quadrant
b)
The curve of a parabola
y
=
−
m
x
2
lies in the I & II quadrant
c)
The curve of a parabola
x
=
−
m
y
2
lies in the I & II quadrant
d)
The curve of a parabola
x
=
−
m
y
2
lies in the II & III quadrant
e)
The curve of a parabola
y
=
m
x
2
lies in the I & II quadrant
(i)
{c,a,d}
(ii)
{a,d}
(iii)
{b,e,d}
(iv)
{b,e}
(v)
{d,e}
Question
27
27.
Which of the following are true for the parabola
y
=
a
x
2
+
b
x
+
c
?
a)
If the curve does not meet the X-axis ,
b
2
−
4
a
c
< 0
b)
If the curve does not meet the X-axis,
there are no real roots for
y
=
a
x
2
+
b
x
+
c
c)
If the curve meets the X-axis at two places, there are two distinct non-real roots.
d)
If the curve meets the X-axis at only one point ,
b
2
−
4
a
c
=
0
e)
If the curve meets the X-axis at only one point ,
b
2
−
4
a
c
>
0
(i)
{e,b}
(ii)
{c,a,b}
(iii)
{a,b,d}
(iv)
{c,a}
(v)
{c,e,d}
Question
28
28.
From the graph, find the approximate values of '
x
' for which
y
=
4
(i)
2.00
,
-2.00
(ii)
1.50
,
-1.50
(iii)
3.00
,
-3.00
(iv)
2.50
,
-2.50
(v)
1.00
,
-1.00
Question
29
29.
From the graph, find the approximate values of '
x
' for which
y
=
-9
(i)
-1.00
,
1.00
(ii)
-0.50
,
0.50
(iii)
-2.00
,
2.00
(iv)
-1.50
,
1.50
(v)
-2.50
,
2.50
Question
30
30.
From the graph, find the approximate values of '
x
' for which
y
=
7
(i)
1.33
,
-5.33
(ii)
1.83
,
-5.83
(iii)
0.83
,
-4.83
(iv)
-0.17
,
-3.83
(v)
0.33
,
-4.33
Question
31
31.
From the graph, find the approximate values of '
x
' for which
y
=
-3
(i)
-2.00
,
0.50
(ii)
-1.00
,
-0.50
(iii)
-1.50
,
0.00
(iv)
-0.50
,
-1.00
(v)
-2.50
,
1.00
Question
32
32.
Which of the following equations represents the given graph ?
(i)
y
=
4
x
2
(ii)
y
=
x
2
(iii)
y
=
3
x
2
(iv)
y
=
2
x
2
(v)
y
=
0
Question
33
33.
Which of the following equations represents the given graph ?
(i)
y
=
(
−
3
x
2
)
(ii)
y
=
0
(iii)
y
=
(
−
2
x
2
)
(iv)
y
=
(
−
5
x
2
)
(v)
y
=
(
−
4
x
2
)
Question
34
34.
Which of the following equations represents the given graph ?
(i)
y
=
(
3
x
2
+
6
x
+
4
)
(ii)
y
=
(
x
2
+
6
x
+
4
)
(iii)
y
=
(
2
x
2
+
3
x
+
4
)
(iv)
y
=
(
2
x
2
+
8
x
+
4
)
(v)
y
=
(
2
x
2
+
6
x
+
4
)
Question
35
35.
Which of the following equations represents the given graph ?
(i)
y
=
(
−
3
x
2
−
5
x
−
3
)
(ii)
y
=
(
−
2
x
2
−
3
x
−
3
)
(iii)
y
=
(
−
x
2
−
5
x
−
3
)
(iv)
y
=
(
−
2
x
2
−
7
x
−
3
)
(v)
y
=
(
−
2
x
2
−
5
x
−
3
)
Question
36
36.
Which of the following equations represents the given graph ?
(i)
x
=
y
2
(ii)
x
=
(
−
y
2
)
(iii)
x
=
3
y
2
(iv)
x
=
5
y
2
(v)
x
=
2
y
2
Question
37
37.
The point
(
5
,
(
−
65
)
)
lies on which of the given parabolae?
(i)
y
=
(
−
3
x
2
+
x
)
(ii)
y
=
(
−
3
x
2
)
(iii)
y
=
(
−
3
x
2
+
5
)
(iv)
y
=
(
−
3
x
2
+
x
+
5
)
Assignment Key
1) (ii)
2) (iii)
3) (iv)
4) (i)
5) (iii)
6) (i)
7) (iv)
8) (iii)
9) (iii)
10) (i)
11) (ii)
12) (iii)
13) (i)
14) (ii)
15) (i)
16) (iv)
17) (ii)
18) (i)
19) (i)
20) (v)
21) (iv)
22) (iii)
23) (iii)
24) (iii)
25) (i)
26) (v)
27) (iii)
28) (i)
29) (iv)
30) (iii)
31) (iii)
32) (iv)
33) (i)
34) (v)
35) (v)
36) (v)
37) (iv)
