Range and Graph of Quadratic Expressions

If $x^2+2ax+10-3a >0$ for all $x \in R$, then

If $f:\left[0,2\right]\to \left[0,2\right]$ is bijective function defined by $f\left(x\right)=a{x}^2+bx+c,$ where $a, b \& c$ are non-zero real numbers, then $f\left(2\right)$ is equal to

If $l, m\left(l<m\right)$ are roots of $a{x}^2+bx+c=0$, then $\underset{x\to a}{\lim }\frac{\left|a{x}^2+bx+c\right|}{a{x}^2+bx+c}=$

If the range of $f\left(x\right)=\frac{x^2+ax+b}{x^2+2x+3}$ is $\left[-5,4\right] a,b\in N$, then the value of $a+b$ is

The range of the function  $f\left(x\right)=\frac{3{\mathrm{x}}^2+9\mathrm{x}+17}{3{\mathrm{x}}^2+9\mathrm{x}+7}$ for all $x\in R$  is

The range of value of $\lambda$ for which the expression$\frac{2x^2-5x+3}{4x-\lambda }$ can take all real values for $x\in R-\left\{\frac{\lambda }{4}\right\}$, is

The range of the expression $\frac{\left(2+x^2\right)}{\left(4-x^2\right)}$ is

Let $f\left(x\right)=a{x}^2+bx+c$ is drawn in adjacent diagram, then correct option(s) is/are -

Find the range of rational expression.

$y=\frac{x+1}{2x-3}$

Find the range of quadratic function $f\left(x\right)=2x^2+12x+16$.

Find the range of quadratic function $f\left(x\right)=-2x^2+4x+2$.

The quadratic expression $a{x}^2+bx+c$ has the same sign as a when the roots of the equation $a{x}^2+bx+c=0 (a\ne 0)$ are real and unequal and $x$ lies between them.

The quadratic expression $a{x}^2+bx+c$ has the same sign as '$a$' when the roots of the equation $a{x}^2+bx+c=0 (a\ne 0)$ are real and unequal and $x$ does not lie between them.

Find the range of the following function:

$f\left(x\right)=x^2+5, x$ is a real number.

Find the range of the following function:

$f\left(x\right)=2-3x^2, x\in R,x>0$

Find the values of $k$ for which exactly one root of the quadratic equation $2x^2–4(k–3)x+k–7=0$ lies in $(0,1)$.

Find the range of $k$ for which $6$ lies between the roots of the quadratic equation $x^2+5(k–3)x+24=0$.

Identify a quadratic expression from the following.

Identify a quadratic expression from the following.