question\nfind the minimum value of the function $f(x) = x^2 + 7.5x + 7.7$ to the nearest hundredth.

Answer:

-4.21

Explanation:

Step1: Identify vertex x-coordinate

For $f(x)=ax^2+bx+c$, $x=-\frac{b}{2a}$ Here $a=1$, $b=7.5$, so $x=-\frac{7.5}{2\times1}=-3.75$

Step2: Compute f(-3.75)

Substitute $x=-3.75$ into $f(x)$: $$f(-3.75)=(-3.75)^2 + 7.5\times(-3.75) + 7.7$$ $$=14.0625 - 28.125 + 7.7$$

Step3: Calculate final value

$$14.0625 - 28.125 + 7.7 = -4.2125$$ Round to nearest hundredth: $-4.21$