Graphical Representation of a Quadratic Equation

Q. The graph of the polynomial f(x) = ax² + bx + c is as shown below (Fig. 2.19). Write the signs of a and b² − 4ac.

Q. Question2 (ii)
Are the following statements ‘True’ or False’? Justify your answer.
ii) If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial

Q. Question 2 (iii)
Are the following statements ‘True’ or False’? Justify your answer.
iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not be a quadratic polynomial

Q. If the graph of quadratic polynomial ax² + bx + c cuts negative direction of y-axis, then what is the sign of c?

Q. Match the graphs to the nature of roots of the quadratic equations involved.
((i), (ii) and (iii) stand for real and distinct roots, no real roots and real and equal roots respectively)

1. $A-\left(iii\right),B-\left(ii\right)$ and $C-\left(i\right)$
2. $A-\left(i\right),B-\left(ii\right)$ and $C-\left(iii\right)$
3. $A-\left(ii\right),B-\left(i\right)$ and $C-\left(ii\right)$
4. $A-\left(i\right),B-\left(iii\right)$ and $C-\left(ii\right)$

Q. The number of real roots of equation ${\log }_{e}x+ex=0$ is

1. $2$
2. $0$
3. $3$
4. $1$

Q. The graph of the equation $3x^2+4x+5$ = 0 intersects the x-axis at point(s).

1. \N
2. 1
3. 2
4. 3

Q. The number of real roots of equation ${\log }_{e}x+ex=0$

1. $0$ (zero)
2. $1$
3. $2$
4. $3$

Q. As per the figure, the graph of $y=p\left(x\right)$ has ................ real zeros.

1. $1$
2. $0$
3. $2$
4. $3$

Q. $(x^2+1{)}^2=0$ has

1. $\text{four real roots}$
2. $\text{two real roots}$
3. $\text{no real root}$
4. $\text{one real root}$

Q. If $a<0$, then the function $f\left(x\right)=a{x}^2+bx+c$ has

1. constant value
2. positive value
3. minimum value
4. maximum value

Q. Identify the ordered pair of the zeroes of the linear polynomials given in the graph?

1. $(14,12)$ and $(5,0)$
2. $(1.8,0)$ and $(11,0)$
3. $(1,5)$ and $(1.8,0)$
4. $(2,-2)$ and $(5,0)$

Q. In the given figure, if the curve is represented by $x^2+x+1$, then the shortest distance of vertex A from the x - axis is

1. 3 units
2. $\frac{1}{2}$ units
3. $\frac{3}{4}$ units
4. 1 unit