Question

Find the maximum value of $5^{-(2x^2-8x+6)}.$

• A. 20
• B. 25
• C. 30
• D. 28

Answer 1

The correct option is B

25

The value of $\left(5^{-y}\right)$ will be maximum when y is minimum.
where, y = $2x^2-8x+6$
y is a quadratic equation of the form $a{x}^2+bx+c$ with a = +2, b= (-8) and c= 6.
When a > 0, the maximum value of y is obtained when $x=\frac{-b}{2a}$.
In our case, a>0, so,
$x=\frac{-(-8)}{(2\times 2)}=2.\to y=(2\times 2^2)-(8\times 2)+6\to y=8-16+6=-2\to y=2$

So,maximum value of $5^{-y}=\left(5^{-(-2)}\right)=25$.