Question

The range of $f\left(x\right)=-x^2+7x+60$ in $x\in [-3,2]$ is

• A. $[30,70]$
• B. $[30,\frac{289}{4}]$
• C. $[70,\frac{289}{4}]$
• D. $[30,\frac{289}{4})$

Answer 1

The correct option is A $[30,70]$

$f\left(x\right)=-x^2+7x+60$
For given function
$a<0,b>0$ and $c=60$
$\therefore$ vertex of $y=f\left(x\right)$ will be in $1^{\text{st}}$ quadrant, so the graph will be

$x$ coordinate of the vertex is
$-\frac{b}{2a}=\frac{7}{2}\notin [-3,2]$
$\because$ Vertex is in right of the given interval.
$\therefore$ Range for given condition is
$\left[f\right(-3),f(2\left)\right]\equiv [30,70]$