Plotting Graph of Quadratic Equation

Q. Select the possible graph(s) of the quadratic equation $y=a{x}^2+bx+c$ where $a<0,D>0.$

1. 
2. 
3. 
4. 

Q.

Which of the following represents the graph of $y=-x^2+6x+1$

1. 

2. 

3. 

4. 

Q. Consider the quadratic polynomial $y=a{x}^2+bx+c$. Select the possible graphs for which $a<0\&D=0.$

1. 
2. 
3. 
4. 

Q. Observe the graph of $y=a{x}^2+bx+c$ and mark the correct statement(s)

1. Roots are equal
2. $D=0$
3. $D>0$
4. $a>0$

Q. The graph of $y=-x^2$ is

1. symmetric about the $y-$axis
2. All of the above
3. symmetric about the $x-$axis
4. Symmetric about the origin

Q. For the given graph of $y=a{x}^2+bx+c$ as shown, select the correct statements.

1. $y>0\forall x\in (-\infty ,\alpha )\cup (\beta ,\infty )$
2. $D>0$
3. $a>0$
4. $y<0\forall x\in (\alpha ,\beta )$

Q. For which of the following graphs of the function $y=a{x}^2+bx+c$, we will get $a>0\&D<0.$

1. 
2. 
3. 
4. 

Q. If $a<0$ and $D<0$, then the graph of $y=a{x}^2+bx+c$
$(\text{where}D=b^2-4ac)$

1. cuts the $x-$axis
2. lies entirely below $x-$axis
3. touches the $x-$axis
4. lies entirely above $x-$axis

Q. The graph of \(f(x)=-x^2+x-2\) is

Q. The graph of the quadratic expression $y=x^2+2x+5$ will be an opening upward parabola.

1. True
2. False

Q. The quadratic polynomial $p\left(x\right)$ has the following properties: $p\left(x\right)\ge 0$ for all real numbers, $p\left(1\right)=0$ and $p\left(2\right)=2$. Then the value of $p\left(3\right)$ is

Q. The graph of $y=x^2$ is symmetric about the $x-$ axis.

1. True
2. False

Q. In the given figure, make correct pair of colours and graphs they represent

1. Blue
2. $y=2x^2$
3. Red
4. $y=\frac{x^2}{2}$
5. Green
6. Black
7. $y=x^2$
8. $y=-x^2$

Q. The curve $y^2(10-x)=x^3$ is symmetric about

Q. The number of integral values of $x$ for which $f\left(x\right)=2x^2-20x+42$ is negative is

Q. The graph of the quadratic expression $y=(-11.5)x^2$ is an upward opening parabola.

1. True
2. False

Q. If $y=x^2+kx+1$ intersects the $x$-axis at two different points, then the minimum positive integral value of $k$ is

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

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

Q. Which among the following is the correct graphical representation of the quadratic polynomial $y=-2x^2+2x-0.5?$

1. 
2. 
3. 
4. 

Q. The number of distinct real roots of
$x^4-4x^3+12x^2+x-1=0$ is

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

Q. For the equation $|x^2-2x-3|=k,$ consider the following statements :
$\left(1\right)$ For $k=-1,$ there is no solution.
$\left(2\right)$ For $k=2,$ there are four solutions.
$\left(3\right)$ For $k=4,$ there are two solutions.
$\left(4\right)$ For $k=0,$ there are two solutions.

the CORRECT statements are

1. $\left(2\right)$ and $\left(4\right)$ only
2. $\left(1\right)$ and $\left(2\right)$ only
3. $\left(1\right),$ $\left(2\right)$ and $\left(4\right)$ only
4. $\left(1\right),$ $\left(2\right)$ and $\left(3\right)$ only

Q. Which among the following is the correct graphical representation of the quadratic polynomial $y=-x^2-2x+3?$

1. 
2. 
3. 
4. 

Q. The number of integral value(s) of $a$ for which ${\log }_e(x^2+5x)={\log }_e(x+a+3)$ has exactly one solution is

1. $4$
2. $1$
3. $2$
4. $5$

Q. Which of the following is NOT the graph of a quadratic polynomial ?

1. 
2. 
3. 
4. 

Q. For the given graphs of quadratic equations $p,q,r,s$, select the quadratic equations for which the coefficient of leading term is negative.

1. $s$
2. $p$
3. $r$
4. $q$

Q. Given the graph of $y=a{x}^2+bx+c$ as shown,
the leading coefficient , and discriminant

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

Q. The graph of $y=-x^2$ is the mirror image of along the $x-$ axis.

1. $y=2x^2$
2. $y=x^2$
3. $y=-2x^2$

Q. For any quadratic equation $y=a{x}^2+bx+c.$ Select the possible graphs for which $a>0.$

1. 
2. 
3. 
4.