Question

The range of the quadratic expression $y=3x^2+8x-3$ is

• A. $\left(-\infty ,-\frac{25}{3}\right)$
• B. $\left(-\frac{100}{3},\infty \right)$
• C. $\left(-\frac{25}{3},\infty \right)$
• D. $\left(-\frac{100}{12},\infty \right)$

Answer 1

The correct option is C $\left(-\frac{25}{3},\infty \right)$

Given quadratic expression is $y=3x^2+8x-3$
On comparing with standard form of quadratic expression $\text{y}=a{x}^2+bx+c$
we get, $a=3,b=8,c=-3$ and $D=b^2-4ac=8^2-\mathrm{4.3.}(-3)=100$

Now, the vertex of the quadratic polynomial is given by:
$(-\frac{b}{2a},-\frac{D}{4a})$
$\because a=3>0$ which means it's an upward opening parabola.
$\Rightarrow$ Range of the quadratic expression is $[-\frac{D}{4a},\infty )$.

$\text{Where}-\frac{D}{4a}=-\frac{100}{4.3}=-\frac{25}{3}$

$\therefore \text{Range}\in [-\frac{25}{3},\infty )$