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Find the minimum value of the function
f(x)=2x^(2)-26.2 x+89.6 to the nearest hundredth.
Answer:

Find the minimum value of the function $f(x)=2 x^{2}-26.2 x+89.6$ 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}-26.2 x+89.6

to the nearest hundredth.

\newline

Answer:

Calculate Vertex: To find the minimum value of the quadratic function $f(x) = 2x^2 - 26.2x + 89.6$ , 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 $b = -26.2$ . $\newline$ $h = -(-26.2) / (2 \times 2) = 26.2 / 4 = 6.55$
Find y-coordinate: Next, we find the y-coordinate of the vertex, $k$ , by substituting the value of $h$ back into the function $f(x)$ . $k = f(6.55) = 2(6.55)^2 - 26.2(6.55) + 89.6$
Perform calculations: Now we perform the calculations for $k$ . $k = 2(6.55)^2 - 26.2(6.55) + 89.6$ $k = 2(42.9025) - 171.61 + 89.6$ $k = 85.805 - 171.61 + 89.6$ $k = -85.805 + 89.6$ $k = 3.795$
Round to nearest hundredth: Since we are asked to round to the nearest hundredth, we round $k$ to $3.80$ .

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