Question

The range of $f\left(x\right)=2x^2-3x+2$ if $x\in [0,2]$ is

• A. $[\frac{7}{8},4]$
• B. $[2,4]$
• C. $[\frac{7}{8},\infty )$
• D. $[2,\infty )$

Answer 1

The correct option is A $[\frac{7}{8},4]$

$f\left(x\right)=2x^2-3x+2$,
$a=2$, $b=-3$, $c=2$
$-\frac{b}{2a}=\frac{3}{4}\in [0,2]$

Now, $f\left(0\right)=2$
$f\left(\frac{3}{4}\right)=\frac{7}{8}\to \text{min}$
$f\left(2\right)=4\to \text{max}$