find the maximum value of the function f(x)= -0.1x² + x - 7.7 to the nearest hundredth. answer

Answer:

$-2.7$

Explanation:

Step1: Identify coefficients

For the quadratic function $f(x)=-0.1x^{2}+x - 7.7$, $a=-0.1$, $b = 1$, $c=-7.7$.

Step2: Find x - coordinate of vertex

The x - coordinate of the vertex of a quadratic function $y = ax^{2}+bx + c$ is $x=-\frac{b}{2a}$. So $x=-\frac{1}{2\times(-0.1)}=\frac{-1}{-0.2}=5$.

Step3: Find the maximum value

Substitute $x = 5$ into the function $f(x)$. $f(5)=-0.1\times5^{2}+5 - 7.7=-0.1\times25 + 5-7.7=-2.5 + 5-7.7=-2.7$.