Find the maximum or minimum value of the Q.E

i) $2x-7-5x^2$    $ii) 3x^2+2x+11$

i) $2x-7-5x^2$

Given equation $2x-7-5x^2$

Compare with $a{x}^2+bx+c$ we get 

$a=-5<0, b=2, c=-7$

If $a<0$the given expression is maximum value 
Maximum value

$$\begin{gathered} =\frac{4ac-b^2}{4a} \\ =\frac{4\left(-5\right)\left(-7\right)-{\left(2\right)}^2}{4\left(-5\right)}=\frac{140-4}{-20} \\ =\frac{-136}{20}=\frac{-34}{5} \end{gathered}$$

ii) Given $3x^2+2x+11, a=3>0, b=2, c=11$

If $a>0$the given expression is maximum value  Minimum  value

Minimum value $=\frac{4ac-b^2}{4a}$

$=\frac{4\left(3\right)\left(11\right)-{\left(2\right)}^2}{4\left(3\right)}=\frac{132-4}{12}=\frac{128}{12}=\frac{32}{3}$