question find the minimum value of the function f(x)=2x² + 9.3x + 3 to the nearest hundredth. answer attempt…

Explanation:

Step1: Identify coefficients

For the quadratic function $f(x)=ax^{2}+bx + c$, here $a = 2$, $b=9.3$, $c = 3$.

Step2: Find x - coordinate of vertex

The x - coordinate of the vertex of a quadratic function is $x=-\frac{b}{2a}$. Substitute $a = 2$ and $b = 9.3$ into the formula: $x=-\frac{9.3}{2\times2}=-\frac{9.3}{4}=- 2.325$.

Step3: Find the minimum value

Substitute $x=-2.325$ into the function $f(x)=2x^{2}+9.3x + 3$. $f(-2.325)=2\times(-2.325)^{2}+9.3\times(-2.325)+3$. First, calculate $(-2.325)^{2}=5.405625$, then $2\times5.405625 = 10.81125$. $9.3\times(-2.325)=-21.6225$. $f(-2.325)=10.81125-21.6225 + 3=-7.81125\approx - 7.81$.

Answer:

$-7.81$