Graphs of Quadratic Equation for different values of D when a>0

Q.

Are there unreal roots in quadratic equations?

Q. The possible graph for $y=a{x}^2+bx+c$ if $a>0$ and $D>0$ is/are ?

1. 
2. 
3. 
4. 

Q. For any quadratic equation $y=a{x}^2+bx+c,$ if $a>0\&D<0,$ then curve will intersect the $x-$ axis at

1. $0$ points.
2. $2$ points.
3. $1$ points.

Q.

What are two different types of graphs of a quadratic function?

Q.

The equation $e^{x-8}+2x-17=0$ has:

1. one real root

2. two real roots

3. eight real roots

4. four real roots

Q. The graph of a quadratic polynomial $f\left(x\right)$ is shown below:


Which of the following options is/are correct?

1. $f(-1)<0$
2. $f\left(2\right)>0$
3. $f(-2)>0$
4. $f\left(1\right)=0$

Q. Consider the function $f\left(x\right)=x^2-4x+17.$ If $M$ and $m$ are the maximum and minimum values of $f$ in $[0,3]$ respectively, then the value of $2M-m$ is

Q. For any quadratic equation $y=a{x}^2+bx+c,$ if $a>0\&D=0,$ then $y<0\forall$

1. $x\in R$
2. $x\in R^{+}$
3. $x\in \varphi$

Q. For the quadratic equation $a{x}^2+bx+c=0.$ Match the following graphs with the conditions given.

1. $a>0,D=0$
2. $a>0,D>0$
3. $a>0,D<0$

Q. For the given graph of the quadratic polynomial $y=a{x}^2+bx+c$ as shown below. Select the correct options.

1. $c<0$
2. $b^2-4ac>0$
3. $a>0$
4. $b>0$

Q. Consider the function $f\left(x\right)=x^2-4x+17.$ If $M$ and $m$ are the maximum and minimum values of $f$ in $[0,3]$ respectively, then the value of $2M-m$ is

Q. The graph of a quadratic polynomial $f\left(x\right)=a{x}^2+bx+c$ is shown below


Which of the following options is/are true for the graph?

1. $9a-3b+c<0$
2. $4a-2b+c<0$
3. $a-b+c>0$
4. $4a-6b+9c>0$

Q.

What can be the shape of graph of $y=2x^2+bx+c$ where $b,c\in R$?

1. 

2. 

3. 

4. Can't say

Q. Consider $f\left(x\right)=a{x}^2+bx+c$ with $a>0$,
If both roots of the quadratic equation are smaller than any constant $k$. The necessary and sufficient condition for this are :

1. $-\frac{b}{2a}<k$
   
2. $D\ge 0$
3. All of the above
4. $f\left(k\right)>0$
   

Q. The possible graph for $y=a{x}^2+bx+c$ if $a>0$ and $D>0$ is/are ?

1. 
2. 
3. 
4. 

Q.

Graph of $y=x^2+7x+3$ intersects the $x$-axis at __ points

Q. For the given quadratic expression $y=a{x}^2+bx+c,$ if $a>0\&D=0,$ then the graph will intersect the $x-$ axis at

1. $2$ points.
2. $1$ point.
3. $0$ points.

Q. The graph of a quadratic polynomial $f\left(x\right)$ is shown below:


Which of the following options is/are correct?

1. $f\left(2\right)>0$
2. $f\left(1\right)=0$
3. $f(-2)>0$
4. $f(-1)<0$

Q. Number of roots of the equation $x^2-2x-{\log }_2|1-x|=3$ is

Q. If the graph of quadratic polynomial $a{x}^2+bx+c$ is


then which of the following is/are correct?

1. $c>0$
2. $D<0$
3. $b<0$
4. $a>0$

Q. For any quadratic expression $y=a{x}^2+bx+c,$ where $a>0\&D<0,y=0$, we have

1. $x\in R^{-}$
2. $x\in \varphi$
3. $x\in R$

Q.

The minimum and maximum values of \(f(x) = {x}^{2}+ 4x +17\) are

Q.

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

1. 

2. 

3. 
   
   

4. 

Q. If the graph of quadratic polynomial $a{x}^2+bx+c$ is


then which of the following is/are correct?

1. $c>0$
2. $b<0$
3. $D<0$
4. $a>0$

Q.

A: The minimum value of '$y$' for the expression $y=2x^2+4x+5$ occur at $x=$______

B: The maximum value of expression $-3x^2+12x+5$ is _______

1. $-1,17$

2. $2,17$

3. $-1,27$

4. $2,27$

Q. For the quadratic equation $a{x}^2+bx+c=0.$ Match the following graphs with the conditions given.

1. $a>0,D=0$
2. $a>0,D<0$
3. $a>0,D>0$

Q. For the quadratic expression $y=a{x}^{2}bx+c,$ choose the correct pair.

1. $g\left(x\right)$
2. $p\left(x\right)$
3. $h\left(x\right)$
4. $f\left(x\right)$
5. $a>0,D=0$
6. $a>0,D<0$
7. $a<0,D>0$
8. $a<0,D<0$

Q.

The range of the expression $f\left(x\right)=3x^2-12x+5$ is

1. $[-7,\infty )$

2. None of these

3. $[-4,\infty )$

4. $(-\infty ,-4]$

Q. For the quadratic expression $y=a{x}^{2}bx+c,$ choose the correct pair.

1. $f\left(x\right)$
2. $g\left(x\right)$
3. $a>0,D=0$
4. $p\left(x\right)$
5. $a<0,D>0$
6. $a>0,D<0$
7. $a<0,D<0$
8. $h\left(x\right)$

Q.

Graph of $y=x^2+7x+3$ intersects the $x$-axis at __ points