To draw the graph of a quadratic polynomial and observe:
(i) The shape of the curve when the coefficient of x2
is positive.
(ii) The shape of the curve when the coefficient of x2
is negative.
(iii) Its number of zeroes.
Answers
Answer:
To find zeroes of a quadratic polynomials graphically.
Aim
To draw the graph of the quadratic polynomial and observe.
i) Shape of the curve when coefficient of
x2
is positive.
ii) Shape of the curve when coefficient of
x2
is negative.
iii) Its number of zeroes.
Materials Required
Graph sheets and maths kit.
Procedure
1. Consider the following quadratic polynomial
p(x)
of the form,
ax2+bx+c
Case I
p(x)=x2+2x+1(a>0)
Case II
p(x)=x2+1−(a>0)
Case III
p(x)=4−x2(a<0)
2. Find ordered pairs for different values of
x
for the three cases and plot them.
3. Join the plotted points by a free hand curve.
Case I:
x2+2x+1
x
0 1 -1 2 -2 -3
y
1 4 0 9 1 4
Case II:
x2+1
x
0 -1 1 2 -2
y
1 2 2 5 5
Case III:
4−x2
x
0 1 -1 2 -2
y
4 3 3 0 0
Observation Table
S.No Polynomial Shape of curve Direction of parabola Coordinates of the point of intersection with
x
-axis Absicca of coordinates Number of zeroes
1
x2+2x+1
Parabola Upward -1, 0 -1 1
2
x2+1
Parabola Upward Nil Nil 0
3
4−x2
Parabola Downward (2, 0) & (-2, 0) -2, 2 2
Conclusion
1. The shape of the curve obtained by drawing the graph of a quadratic polynomial is a parabola.
2. When coefficient of
x2
is positive
(a>0)
. The parabola open upwards.
3. When coefficient of
x2
is negative
(a<0)
. The parabola opens downwards.
4. A polynomial of degree 2 is a quadratic polynomial has at most 2 zeroes