Question

Q.2 To draw the graph of a quadratic polynomial and observe:
(1) The shape of the curve when the cofficient of x2 is positive.
(ii) The shape of the curve when the cofficient of x? is negative.
(ii) It number of zero.​

Answer 1

Answer:

Step-by-step explanation:

Our question is: Q.2 To draw the graph of a quadratic polynomial and observe:

(1) The shape of the curve when the cofficient of x2 is positive.

(ii) The shape of the curve when the cofficient of x? is negative.

(ii) It number of zero.

We have that you want to draw a graph of a quadratic polynomial. Then we should consider that we are dealing with a parabola. Since it is quite difficult to answer you graphically here, I can explain you the process you need to follow in order to reach your aim.

Lets consider f(x) = a * x^2, a real number.

If a is positive, our parabola will be facing up.

If not, if it is negative it will be facing down.

In case it is zero we can conclude that it is no more a parabola and it depends on the other coefficients. It may be a linear function or also a constant function.

I hope this helps your studies!!

Keep it up!!

Answer 2

Answer: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.

Step-by-step explanation: