Ncert Activities Maths problems:- 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
Solutions -
1.)When the coefficient of x2 is positive, the graph of the quadratic polynomial is a positive.
The shape of the curve when the coefficient of x2 is positive parabola that opens upwards. This is because the parabola is a reflection of the graph of y = x2 about the x-axis. The parabola will have two zeroes, which are the point where the graph crosses the x-axis.
2.)The shape of the curve when the coefficient of x2 is negative
When the coefficient of x2 is negative, the graph of the quadratic polynomial is a parabola that opens downwards. This is because the parabola is a reflection of the graph of y = -x2 about the x-axis. The parabola will have two zeroes, which are the
points where the graph crosses the x-axis.
3.) Its number of zeroes
The number of zeroes of a quadratic polynomial is equal to the degree of the polynomial. The degree of a polynomial is the highest power of the variable in the polynomial. In the case of a quadratic polynomial, the degree is 2. Therefore, a quadratic polynomial will have 2 zeroes.
Hope this helps you!
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
Solutions -
The shape of the curve when the coefficient of x2 is positive parabola that opens upwards. This is because the parabola is a reflection of the graph of y = x2 about the x-axis. The parabola will have two zeroes, which are the point where the graph crosses the x-axis.
When the coefficient of x2 is negative, the graph of the quadratic polynomial is a parabola that opens downwards. This is because the parabola is a reflection of the graph of y = -x2 about the x-axis. The parabola will have two zeroes, which are the
points where the graph crosses the x-axis.
The number of zeroes of a quadratic polynomial is equal to the degree of the polynomial. The degree of a polynomial is the highest power of the variable in the polynomial. In the case of a quadratic polynomial, the degree is 2. Therefore, a quadratic polynomial will have 2 zeroes.
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