Graph of Quadratic Expression

Q. If $\frac{(x^2-1)(x+2)(x+1{)}^2}{(x-2)}<0$ , then x lies in the interval

1. (-2, -1) ∪ (1, 2)
2. (-∞, -2) ∪ (2, ∞)
3. (-2, -1) ∪ (2, ∞)
4. (-2, -1) ∪ (1, ∞)

Q. Let S be the set of values of 'a' for which 2 lie between the roots of quadratic equation $x^2+(a+2)x-(a+3)=0$. Then S is given by

1. (5, ∞)
2. (-∞, -5]
3. [5, ∞)
   
4. (-∞, -5)

Q.

What is the vertex of the quadratic function y = $x^2-6x+12$?

1. (1, 1)

2. (2, 2)

3. (2, 3)

4. (3, 3)

Q.

If a, b, c $ϵ$ R and a $\ne$ 0, c > 0, the graph of $f\left(x\right)$ = $a{x}^2+bx+c$ for which $f\left(x\right)=0$ has only imaginary roots, will look like

1. 

2. 

3. 

4. 

Q. The number of solutions of the equation $x^3+2x^2+5x+2cosx=0$ in $[0,2\pi ]$ is

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

Q.
The diagram shows the graph of $y=a{x}^2+bx+c$. Then

1. a > 0
2. b < 0
3. b² - 4ac = 0
4. c < 0

Q.

Pick the correct plot for the function $y=x^2-2x+6$

1. 

2. 

3. 

4. 
   
   

Q.

Plot the graph of $y=($x-3${)}^2+7$

1. 

2. 

3. 

4. 

Q.

If a, b, c $\in$ R and a $\ne$ 0, c < 0, and if the quadratic equation $a{x}^2+bx+c$ = 0 has imaginary roots, then a + b + c is

1. Can't say

2. Zero

3. Negative

Q.

Which among the following is the correct graphical representation of $y=-x^2+4x+1$ ?

1. 

2. 

3. 

4.