Question

The range of the quadratic expression $y=-4x^2+13x-3$ is

• A. $(-\infty ,\frac{121}{2}]$
• B. $(-\infty ,\frac{121}{4}]$
• C. $(-\infty ,\frac{121}{16}]$
• D. $(-\infty ,\frac{121}{8})$

Answer 1

The correct option is C $(-\infty ,\frac{121}{16}]$

Given :$\text{y}=-4x^2+13x-3$
By comparing with the standard form $y=a{x}^2+bx+c$
We have $a=-4,b=13,c=-3$.
Here, $a<0\Rightarrow$ it is a downward opening parabola and we know the vertex of downward opening parabola i.e. $(-\frac{b}{2a},-\frac{D}{4a})$.
Therefore the range of the quadratic expression is $(-\infty ,-\frac{D}{4a}]$.

$\therefore D=b^2-4ac={13}^2-4.(-4).(-3)$
$\Rightarrow D=121$
Hence, $-\frac{D}{4a}=-\frac{121}{4.(-4)}=\frac{121}{16}$
$\therefore Range\in (-\infty ,\frac{121}{16}]$