finding maximum/minimum values with tec question find the minimum value of the function f(x)=x² + 7.1x + 19…

finding maximum/minimum values with tec question find the minimum value of the function f(x)=x² + 7.1x + 19 to the nearest hundredth. answer attempt 1 out of 2

finding maximum/minimum values with tec question find the minimum value of the function f(x)=x² + 7.1x + 19 to the nearest hundredth. answer attempt 1 out of 2

Answer

Answer:

$6.39$

Explanation:

Step1: Identify coefficients

For the quadratic function $f(x)=ax^{2}+bx + c$, here $a = 1$, $b=7.1$, $c = 19$.

Step2: Find x - coordinate of vertex

The x - coordinate of the vertex of a quadratic function is $x=-\frac{b}{2a}$. Substitute $a = 1$ and $b = 7.1$ into the formula: $x=-\frac{7.1}{2\times1}=-3.55$.

Step3: Find the minimum value

Substitute $x=-3.55$ into the function $f(x)=x^{2}+7.1x + 19$. $f(-3.55)=(-3.55)^{2}+7.1\times(-3.55)+19$ $=12.6025-25.205 + 19$ $=6.3975\approx6.39$ (rounded to the nearest hundredth).