find the minimum value of the function $f(x)=1.7x^{2}-7.1x + 13.3$ to the nearest hundredth.

Explanation:

Step1: Identify coefficients

For the quadratic function $f(x)=ax^{2}+bx + c$, here $a = 1.7$, $b=-7.1$, $c = 13.3$.

Step2: Find x - coordinate of vertex

The x - coordinate of the vertex of a quadratic function is $x=-\frac{b}{2a}$. Substitute $a = 1.7$ and $b=-7.1$ into the formula: $x=-\frac{-7.1}{2\times1.7}=\frac{7.1}{3.4}\approx2.09$.

Step3: Find the minimum value

Substitute $x\approx2.09$ into the function $f(x)=1.7x^{2}-7.1x + 13.3$. $f(2.09)=1.7\times(2.09)^{2}-7.1\times2.09 + 13.3$ $=1.7\times4.3681-14.839+13.3$ $=7.42577-14.839 + 13.3$ $=5.88677\approx5.89$.

Answer:

$5.89$