Question
Find the maximum value of the function
f(x) = -1.8^2 - 25.5x -96.2 to the nearest hundredth
f(x) = -1.8^2 - 25.5x -96.2 to the nearest hundredth
Answers
GPT 3.5
To find the maximum value of the function, we need to determine the vertex of the parabola representing the function.
The equation of the function is in the form of a quadratic equation: f(x) = ax^2 + bx + c.
The vertex of the parabola is given by the coordinates (-b/2a, f(-b/2a)).
In this case, a = -1.8, b = -25.5, and c = -96.2.
The x-coordinate of the vertex (-b/2a) can be found using the formula x = -b/2a:
x = -(-25.5)/(2*(-1.8))
= 25.5/3.6
≈ 7.08
Now we substitute this x-coordinate back into the function to find the corresponding y-coordinate:
f(7.08) = (-1.8)^2 - 25.5(7.08) - 96.2
= 3.24 - 180.54 - 96.2
≈ -273.5
Therefore, the maximum value of the function is approximately -273.5.
The equation of the function is in the form of a quadratic equation: f(x) = ax^2 + bx + c.
The vertex of the parabola is given by the coordinates (-b/2a, f(-b/2a)).
In this case, a = -1.8, b = -25.5, and c = -96.2.
The x-coordinate of the vertex (-b/2a) can be found using the formula x = -b/2a:
x = -(-25.5)/(2*(-1.8))
= 25.5/3.6
≈ 7.08
Now we substitute this x-coordinate back into the function to find the corresponding y-coordinate:
f(7.08) = (-1.8)^2 - 25.5(7.08) - 96.2
= 3.24 - 180.54 - 96.2
≈ -273.5
Therefore, the maximum value of the function is approximately -273.5.