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

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

1. $a<0\&D<0$
2. $a<0\&D<0$
3. $a<0\&D>0$

Q. For a quadratic expression $f\left(x\right)=a{x}^2+bx+c,f\left(\alpha \right)=0$
$f\left(x\right)<0\forall x\in R-\left\{\alpha \right\},$ then $a$ , and $D$ .

1. $<0$
2. $\in R$
3. $>0$
4. $=0$

Q. The condition for which the quadratic equation $(p^2-3p+2)x^2+(p^2-4)x+(p-1)=0$ will have a graph which is a downward opening parabola is

1. $p\in R$
2. $p\in (1,2)$
3. $p\in (-\infty ,1)\cup (2,\infty )$
4. $p\in (-\infty ,-1)\cup (2,\infty )$

Q. For any quadratic expression $y=a{x}^2+bx+c,$ if $a<0\&D>0,$ then it's graph will intersect the $x-$ axis at $1$ point.

1. False
2. True

Q. For a quadratic expression $y=f\left(x\right)=a{x}^2+bx+c,$ if $f\left(\alpha \right)=0$ and for the rest of values of $x,f\left(x\right)<0.$
Then $a$ , and $D$ .

1. $=0$
2. $>0$
3. $\in R$
4. $<0$

Q. The condition for which the quadratic equation $(p^2-3p+2)x^2+(p^2-4)x+(p-1)=0$ will have a graph which is a downward opening parabola is

1. $p\in (-\infty ,1)\cup (2,\infty )$
2. $p\in R$
3. $p\in (1,2)$
4. $p\in (-\infty ,-1)\cup (2,\infty )$

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


Which of the following options is/are correct?

1. $f\left(0\right)>0$
2. $f\left(3\right)>0$
3. $f(-7)=0$
4. $f(-3)>0$

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


Which of the following options is/are correct?

1. $f(-3)>0$
2. $f\left(3\right)>0$
3. $f\left(0\right)>0$
4. $f(-7)=0$

Q.

The minimum value of $f\left(x\right)=-2x^2+5x+4\forall x\in [0,3]$ is __

Q. Consider the graph of the quadratic polynomial $y=a{x}^2+bx+c$ as shown below.

Which among the following is/are correct?

1. $\frac{a-b+c}{abc}=0$
2. $abc(9a+3b+c)<0$
3. $abc(a-3b+9c)>0$
4. $\frac{a+3b+9c}{abc}<0$

Q.

The graph of expression $f\left(x\right)=-2x^2+5x+7$ looks like:

1. Can’t say

2. Cap shaped parabola

3. A straight line

4. Cup shaped parabola

Q. For any quadratic function $y=-x^2+2x-3,y>0\forall$

1. $x\in R-\left(0\right\}$
2. $x\in \varphi$
3. $x\in R$

Q. For any quadratic function $y=-x^2+2x-3,y>0\forall$

1. $x\in R$
2. $x\in R-\left(0\right\}$
3. $x\in \varphi$

Q. The condition for which the quadratic equation $(p^2-3p+2)x^2+(p^2-4)x+(p-1)=0$ will have a graph which is an upward opening parabola is

1. $p\in (1,2)$
2. $p\in R$
3. $p\in (-\infty ,-1)\cup (2,\infty )$
4. $p\in (-\infty ,1)\cup (2,\infty )$

Q. For$f\left(x\right)=a{x}^2+bx+c,a\ne 0,$ the conditions for which the graph is a downward opening parabola and $f\left(x\right)=0$ have a unique root with multiplicity $2$ is

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

Q.

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

1. 

2. 

3. 

4. 

Q. Let $f\left(x\right)=\frac{a{x}^2+2(a+1)x+9a+4}{x^2-8x+32}$ and $g\left(x\right)=x-x^2-1.$ If $f\left(x\right)$ is less than $M+\frac{3}{4}$ for all $x\in R,$ where $M$ is the maximum value of $g\left(x\right),$ then set of values of $a$ lies in

1. $(-\infty ,\frac{-1}{2}]$
2. $(-\infty ,\frac{-1}{2})$
3. $(-\infty ,-5)$
4. $(-\infty ,0)$

Q. By considering the graph of quadratic polynomial $y=a{x}^2+bx+c$ as shown below.

Which among the following conclusions is/are correct?

1. $abc(9a+3b+c)<0$
2. $abc(a-3b+9c)>0$
3. $\frac{a-b+c}{abc}=0$
4. $\frac{a+3b+9c}{abc}<0$

Q. For$f\left(x\right)=a{x}^2+bx+c,a\ne 0,$ the conditions for which the graph is a downward opening parabola and $f\left(x\right)=0$ have a unique root with multiplicity $2$ is

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

Q. The condition for which the quadratic equation $(p^2-3p+2)x^2+(p^2-4)x+(p-1)=0$ will have a graph which is a downward opening parabola is

1. $p\in (-\infty ,1)\cup (2,\infty )$
2. $p\in (1,2)$
3. $p\in (-\infty ,-1)\cup (2,\infty )$
4. $p\in R$

Q.

The equation $a{x}^2+bx+c=0$ does not have real roots and $c<0$. Which of these is true?

1. $b>a+c$

2. Both $\left(a\right)$ & $\left(b\right)$

3. $4a+2b+c<0$

4. $a+b+c>0$

Q. For any quadratic expression $y=a{x}^2+bx+c,$ if $a<0\&D>0,$ then it's graph will intersect the $x-$ axis at $1$ point.

1. True
2. False

Q.

The graph of expression $f\left(x\right)=-2x^2+5x+7$ looks like:

1. Cap shaped parabola

2. Can’t say

3. Cup shaped parabola

4. A straight line

Q.

The minimum value of $f\left(x\right)=-2x^2+5x+4\forall x\in [0,3]$ is __

Q.

If the graph of $y=3x^2+2\sqrt{b}x+5$ does not touch $x$-axis, which of the following is true?

1. $b>50$

2. $b>15$

3. $b<50$

4. $b<15$

Q. By considering the graph of quadratic polynomial $y=a{x}^2+bx+c$ as shown below.

Which among the following conclusions is/are correct?

1. $\frac{a-b+c}{abc}=0$
2. $\frac{a+3b+9c}{abc}<0$
3. $abc(9a+3b+c)<0$
4. $abc(a-3b+9c)>0$

Q.

The expression $-5x^2+4x+3$, has

1. Maximum value as $\frac{19}{5}$

2. Maximum value at $x=\frac{2}{5}$

3. Minimum value as $\frac{-19}{5}$

4. Minimum value at $x=\frac{2}{5}$

Q. For any quadratic function $y=-x^2+2x-3,y>0\forall$

1. $x\in \varphi$
2. $x\in R$
3. $x\in R-\left(0\right\}$

Q.

The expression $-5x^2+4x+3$, has

1. Maximum value at $x=\frac{2}{5}$

2. Maximum value as $\frac{19}{5}$

3. Minimum value at $x=\frac{2}{5}$

4. Minimum value as $\frac{-19}{5}$