Question

For any quadratic expression $f\left(x\right)=a{x}^2+bx+c,a<0$ and if $(v,f(v\left)\right)$ is it's vertex, then $y\in$

• A. $\left[f\right(v),\infty )$
• B. $[-f(v),f(v\left)\right]$
• C. $(-\infty ,f(v\left)\right]$

Answer 1

The correct option is C $(-\infty ,f(v\left)\right]$

Given quadratic polynomial $f\left(x\right)=a{x}^2+bx+c,a<0$
$\Rightarrow$ The graph is an downward opening parabola as shown:

Here, we know for any quadratic expression with $a<0,$ it's vertex will be the point of maximum.
Thus, it's range $y\in (-\infty ,f(v\left)\right].$