Question

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

Answer 1

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

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

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

$\therefore \text{Range }\in \left[-\dfrac{25}{3}, \infty\right) $