Representing Equations on a Graph

Q.

Polynomials in Real Life

Polynomials are everywhere. It is found in a roller coaster of an amusement park, the slope of a hill, the curve of a bridge or the continuity of a mountain range. They play a key role in the study of algebra, in analysis and on the whole many mathematical problems involving them.

Based on the given information, answer the following question:

If the roller coaster is represented by the following graph $y=p\left(x\right)$ , then name the type of the polynomial it traces.

1. Linear
2. Quadratic
3. Cubic
4. Bi-quadratic

Q. Find the signs of a, b and c in given graph of polynomial, $f\left(x\right)=a{x}^2+bx+c,wherea\ne 0.$

1. 
   $a>0,b=0andc<0$
2. 
   $a>0,b>0andc<0$
3. 
   $a<0,b=0andc<0$
4. 
   $a<0,b=0andc<0$

Q. Find the sign of a, b and c in the below graph of polynomial $f\left(x\right)=a{x}^2+b$.

1. 
   $a>0,b<0andc>0$
2. 
   $a>0,b>0andc>0$
3. 
   $a<0,b<0andc>0$
4. 
   $a>0,b>0andc<0$

Q. Three curves i.e.
a) $y=-x^2$
b) $y=-x^3$
c) $y=-x^7$
are depicted in the following graph and are numbered from 1 to 3.

Identify the correct relation.

1. (a)-(1) , (b)-(2), (c)-(3)
2. (a)-(3) , (b)-(2), (c)-(1)
3. (a)-(1) , (b)-(3), (c)-(2)
4. (a)-(2) , (b)-(3), (c)-(1)

Q. The graph given below shows graphical representation of the following polynomials.

a) $y=x^3$
b) $y=x^7$
c) $y=x^2$
d) $y=x^6$


Identify the correct relation between the graphs $\left(1\text{to}4\right)$ and the polynomials $\left(a\text{to}d\right)$.

1. $\left(a\right)-1,\left(b\right)-4,\left(c\right)-3,\left(d\right)-2$
2. $\left(a\right)-2,\left(b\right)-1,\left(c\right)-3,\left(d\right)-4$
3. $\left(a\right)-1,\left(b\right)-2,\left(c\right)-3,\left(d\right)-4$
4. $\left(a\right)-4,\left(b\right)-3,\left(c\right)-1,\left(d\right)-2$

Q.
The number of zeroes of a polynomial represented in the given graph is _______.

1. 3

Q. Find the number of zeros of the quadratic polynomial f(x)=x^2-2√a x+(a-b). Verify the relationship between zeroes and coefficients.

Q. Draw the graph of $y=2x^2$ and hence solve $2x^2+x-6=0$ .

1. {2, 1.5}
2. {-2, 1.5}
3. {2, -1.5}
4. {-2, -1.5}

Q. The graph given below shows graphical representation of the following polynomials.

a) $y=x^3$
b) $y=x^7$
c) $y=x^2$
d) $y=x^6$


Identify the correct relation between the graphs $\left(1\text{to}4\right)$ and the polynomials $\left(a\text{to}d\right)$.

1. $\left(a\right)-1,\left(b\right)-4,\left(c\right)-3,\left(d\right)-2$
2. $\left(a\right)-2,\left(b\right)-1,\left(c\right)-3,\left(d\right)-4$
3. $\left(a\right)-1,\left(b\right)-2,\left(c\right)-3,\left(d\right)-4$
4. $\left(a\right)-4,\left(b\right)-3,\left(c\right)-1,\left(d\right)-2$

Q. The graph of a polynomial P(x) is as shown. The number of zeroes is/are

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

Q. Find the number of zeroes of the polynomial from the graph given below.

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

Q. Three curves i.e.
a) $y=x^3$
b) $y=x^5$
c) $y=x^7$
are plotted on the following graph.
Which polynomial is represented by graph 1?

1. $y=x^3$
2. $y=x^5$
3. $y=x^7$
4. None of the above

Q. A quadratic polynomial has no zero.Its graph.....

1. touches $X$-axis at any point
2. does not intersect $X$-axis at any points.
3. is in any one half plane of $X$-axis
4. intersects $X$ -axis at two distinct points

Q.
The number of zeroes of a polynomial represented in the given graph is _______.

1. 3

Q. Which of the following represents the vertex points of the curve obtained by plotting $y=2x^2$?

1. {0, 0}
2. {0, 7}
3. {7, 0}
4. None of these

Q. Three curves i.e.
a) $y=x^3$
b) $y=x^5$
c) $y=x^7$
are plotted on the following graph.
Which polynomial is represented by graph 1?

1. $y=x^3$
2. $y=x^5$
3. $y=x^7$
4. None of the above

Q. The graph of a linear equation will be:

1. parabolic
2. staight line
3. exponential
4. logarithmic

Q. Which of the following is/are true about the nature of the curve obtained for the polynomial $y=a{x}^2+bx+c$ when a=1, b=-2, c=-3.

1. Curve is open upward
2. Curve is open downward
3. Curve lies above and on the line $y=-4$
4. Curve is symmetrical about $x=1$

Q. Three curves i.e.
a) $y=-x^2$
b) $y=-x^3$
c) $y=-x^7$
are depicted in the following graph and are numbered from 1 to 3.

Identify the correct relation.

1. (a)-(1) , (b)-(2), (c)-(3)
2. (a)-(3) , (b)-(2), (c)-(1)
3. (a)-(1) , (b)-(3), (c)-(2)
4. (a)-(2) , (b)-(3), (c)-(1)

Q. The graph of a polynomial P(x) is as shown. The number of zeroes is/are

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

Q. What do we mean by REAL zeroes of a polynomial ? Is there something called unreal zeroes i.e zeroes which are not real ? If so what is the difference between the both??

Q. The graph given below shows graphical representation of the following polynomials.

a) $y=x^3$
b) $y=x^7$
c) $y=x^2$
d) $y=x^6$


Identify the correct relation between the graphs $\left(1\text{to}4\right)$ and the polynomials $\left(a\text{to}d\right)$.

1. $\left(a\right)-1,\left(b\right)-4,\left(c\right)-3,\left(d\right)-2$
2. $\left(a\right)-2,\left(b\right)-1,\left(c\right)-3,\left(d\right)-4$
3. $\left(a\right)-1,\left(b\right)-2,\left(c\right)-3,\left(d\right)-4$
4. $\left(a\right)-4,\left(b\right)-3,\left(c\right)-1,\left(d\right)-2$

Q. ________ is the degree of the multivariate polynomial $4xy+x^2{y}^2+x^2{y}^4+1.$

1. 6

Q. Three curves i.e.
a) $y=x^2$
b) $y=x^4$
c) $y=x^6$
are depicted in the graph shown below. Which of the polynomials does the graph 3 represent?

1. $y=x^2$
2. $y=x^4$
3. $y=x^6$
4. All of the above

Q. The graph of certain polynomials are given here. Match the graph to the degree of the polynomial.

1. 3
2. 4
3. 5

Q. The sum of the first 5 triangular numbers is equal to:

1. 35
2. 50
3. 16
4. 25

Q. The graph of a polynomial f(x) is as shown in the figure The number of real zeroes of f(x) is ______

1. 1
2. 2
3. 3
4. 4

Q. If a polynomial p(x) is of degree “n”, the graph of the polynomial should cut the X axis at “n” points.

1. True
2. False

Q. Three curves i.e.
a) $y=x^3$
b) $y=x^5$
c) $y=x^7$
are plotted on the following graph.
Which polynomial is represented by graph 1?

1. $y=x^3$
2. $y=x^7$
3. $y=x^5$
4. None of the above

Q. What is the graph of polynomial with degree 2?

1. Line
2. Parabola
3. Circular
4. Curve