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Find the maximum value of the function
f(x)=-0.6x^(2)+3.5 x-13 to the nearest hundredth.
Answer:

Find the maximum value of the function $f(x)=-0.6 x^{2}+3.5 x-13$ to the nearest hundredth. $\newline$ Answer:

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Find trigonometric functions using a calculator

Full solution

Q. Find the maximum value of the function

f(x)=-0.6 x^{2}+3.5 x-13

to the nearest hundredth.

\newline

Answer:

Find Vertex: To find the maximum value of the quadratic function $f(x) = -0.6x^2 + 3.5x - 13$ , we need to find the vertex of the parabola. Since the coefficient of $x^2$ is negative, the parabola opens downwards, and the vertex will give us the maximum value. The $x$ -coordinate of the vertex can be found using the formula $-\frac{b}{2a}$ , where $a$ is the coefficient of $x^2$ and $b$ is the coefficient of $x$ .
Calculate x-coordinate: First, we calculate the x-coordinate of the vertex using the formula $-\frac{b}{2a}$ . Here, $a = -0.6$ and $b = 3.5$ .
x-coordinate of vertex = $-\frac{b}{2a}$ = $-\frac{3.5}{2 \times -0.6}$ = $-\frac{3.5}{-1.2}$ = $2$ . $916666$ ...
Round $x$ -coordinate: Now, we round the $x$ -coordinate to the nearest hundredth, which gives us $2.92$ .
Find y-coordinate: Next, we need to find the y-coordinate of the vertex by substituting $x = 2.92$ into the function $f(x)$ . $f(2.92) = -0.6(2.92)^2 + 3.5(2.92) - 13$
Perform calculations: We perform the calculations: $\newline$ $f(2.92) = -0.6(8.5264) + 10.22 - 13$ $\newline$ $f(2.92) = -5.11584 + 10.22 - 13$ $\newline$ $f(2.92) = 5.10416 - 13$ $\newline$ $f(2.92) = -7.89584$
Round y-coordinate: Finally, we round the y-coordinate to the nearest hundredth to find the maximum value of the function. $\newline$ Maximum value of $f(x) \approx -7.90$

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