Question

Range of the function $f\left(x\right)=2x^2+12x+16$ is

• A. $[-2,\infty )$
• B. $(-\infty ,2]$
• C. $[2,\infty )$
• D. $(-\infty ,-2]$

Answer 1

The correct option is A $[-2,\infty )$

Given quadratic expression is $y=2x^2+12x+16$
On comparing with standard form of quadratic expression $\text{y}=a{x}^2+bx+c,$ we get:
$a=2,b=12,c=16$
$\&D=b^2-4ac=(12{)}^2-4\cdot 2\cdot 16=16$

Now, the vertex of the quadratic polynomial is given by:
$(-\frac{b}{2a},-\frac{D}{4a})$

$\because a=2>0$ This means it's an upward opening parabola.
$\Rightarrow$ Range of the quadratic expression: $[-\frac{D}{4a},\infty )$

$\text{Where}-\frac{D}{4a}=-\frac{16}{4.2}=-2$

$\therefore \text{Range}\in [-2,\infty )$