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Find the minimum value of the function
f(x)=2x^(2)-8.1 x+14.5 to the nearest hundredth.
Answer:

Find the minimum value of the function $f(x)=2 x^{2}-8.1 x+14.5$ to the nearest hundredth. $\newline$ Answer:

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Find trigonometric functions using a calculator

Full solution

Q. Find the minimum value of the function

f(x)=2 x^{2}-8.1 x+14.5

to the nearest hundredth.

\newline

Answer:

Calculate Vertex: To find the minimum value of the quadratic function $f(x) = 2x^2 - 8.1x + 14.5$ , we can use the vertex formula. The vertex of a parabola given by $f(x) = ax^2 + bx + c$ is at the point $(h, k)$ , where $h = -\frac{b}{2a}$ . Since the coefficient of $x^2$ is positive, the parabola opens upwards, and the vertex represents the minimum point.
Find x-coordinate: First, we calculate the x-coordinate of the vertex, $h$ , using the formula $h = -b/(2a)$ . Here, $a = 2$ and $b = -8.1$ . $\newline$ $h = -(-8.1) / (2 \times 2) = 8.1 / 4 = 2.025$
Substitute $x$ into function: Next, we substitute $x = h$ into the function to find the y-coordinate of the vertex, $k$ , which will give us the minimum value of the function. $\newline$ $f(2.025) = 2(2.025)^2 - 8.1(2.025) + 14.5$
Perform calculations: Now we perform the calculations: $\newline$ $f(2.025) = 2(4.100625) - 16.4025 + 14.5$ $\newline$ $f(2.025) = 8.20125 - 16.4025 + 14.5$ $\newline$ $f(2.025) = 6.29875$
Round to nearest hundredth: Finally, we round the minimum value to the nearest hundredth. The minimum value of the function $f(x)$ to the nearest hundredth is $6.30$ .

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