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Find the maximum value of the function
f(x)=-0.3x^(2)+1.2 x-7 to the nearest hundredth.
Answer:

Find the maximum value of the function $f(x)=-0.3 x^{2}+1.2 x-7$ 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)=-0.3 x^{2}+1.2 x-7

to the nearest hundredth.

\newline

Answer:

Quadratic Function Form: The function $f(x) = -0.3x^2 + 1.2x - 7$ is a quadratic function in the form of $f(x) = ax^2 + bx + c$ , where $a = -0.3$ , $b = 1.2$ , and $c = -7$ . Since the coefficient of $x^2$ is negative ( $a = -0.3$ ), the parabola opens downwards, which means the vertex of the parabola will give us the maximum value of the function.
Find Vertex x-coordinate: To find the x-coordinate of the vertex, we use the formula $-\frac{b}{2a}$ . Plugging in the values of $a$ and $b$ , we get $-\frac{1.2}{2 \times -0.3}$ .
Calculate Vertex x-coordinate: Calculating the x-coordinate of the vertex: $-1.2 / (2 \times -0.3) = -1.2 / -0.6 = 2$ .
Find Maximum Value: Now that we have the $x$ -coordinate of the vertex, we can find the maximum value of the function by plugging $x = 2$ into the function $f(x)$ .
Substitute $x = 2$ : Substitute $x = 2$ into the function: $f(2) = -0.3(2)^2 + 1.2(2) - 7$ .
Calculate $f(2)$ : Calculate the value of $f(2)$ : $f(2) = -0.3(4) + 2.4 - 7 = -1.2 + 2.4 - 7 = 1.2 - 7 = -5.8$ .
Maximum Value: The maximum value of the function to the nearest hundredth is $-5.80$ .

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