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Find the maximum value of the function
f(x)=-1.7x^(2)+5x-0.9 to the nearest hundredth.
Answer:

Find the maximum value of the function $f(x)=-1.7 x^{2}+5 x-0.9$ 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)=-1.7 x^{2}+5 x-0.9

to the nearest hundredth.

\newline

Answer:

Find Vertex: To find the maximum value of the quadratic function $f(x) = -1.7x^2 + 5x - 0.9$ , 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, $a = -1.7$ and $b = 5$ .
x-coordinate of the vertex = $-\frac{b}{2a}$ = $-\frac{5}{2 \times -1.7}$ = $-\frac{5}{-3.4}$ = $1$ . $47058823529$ ...
Round x-coordinate: Now we round the x-coordinate to the nearest hundredth. $\newline$ $x$ -coordinate of the vertex $\approx 1.47$
Substitute $x$ into function: Next, we substitute $x = 1.47$ into the function to find the $y$ -coordinate of the vertex, which will give us the maximum value of the function. $\newline$ $f(1.47) = -1.7(1.47)^2 + 5(1.47) - 0.9$
Calculate y-coordinate: We perform the calculations: $\newline$ $f(1.47) = -1.7(2.1609) + 7.35 - 0.9$ $\newline$ $f(1.47) = -3.67353 + 7.35 - 0.9$ $\newline$ $f(1.47) = 3.67647 - 0.9$ $\newline$ $f(1.47) = 2.77647$
Round maximum value: Finally, we round the maximum value to the nearest hundredth. $\newline$ Maximum value of $f(x) \approx 2.78$

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