Find the minimum or maximum value of f(x)=−0.25x2+4x−18
Sow steps for 5x - 3y equals 0 to determine if this is a direct variation
Show steps for 5x - 3y equals 0 to determine if this is a direct variation
This was wrong
Well, let's find the value of x where the minimum or maximum occurs by using the formula x = -b/2a. In this case, a = -0.25 and b = 4.
Plugging these values into the formula, we get x = -4/(2*-0.25) = -4/(-0.5) = 8.
Now, let's substitute x = 8 back into the equation to find the corresponding value of f(x):
f(8) = -0.25(8)^2 + 4(8) - 18 = -0.25(64) + 32 - 18 = -16 + 32 - 18 = -2.
So, the minimum or maximum value of f(x) = -0.25x^2 + 4x - 18 is -2.
But hey, don't take my word for it, maybe f(x) secretly yearns for a more meaningful existence than being confined to a numerical value!
To find the minimum or maximum value of the function f(x) = -0.25x^2 + 4x - 18, we can use the process of finding the vertex of the parabola represented by the quadratic equation.
The vertex of a parabola in the form f(x) = ax^2 + bx + c is given by the coordinates (-b/2a, f(-b/2a)). In this case, a = -0.25, b = 4, and c = -18.
Step 1: Find the x-coordinate of the vertex:
x = -b/2a
x = -4 / (2 * (-0.25))
x = -4 / -0.5
x = 8
Step 2: Find the y-coordinate of the vertex:
f(x) = -0.25x^2 + 4x - 18
f(8) = -0.25(8)^2 + 4(8) - 18
f(8) = -0.25(64) + 32 - 18
f(8) = -16 + 32 - 18
f(8) = -2
Therefore, the vertex of the parabola is (8, -2). The y-coordinate of the vertex represents the minimum or maximum value of the function.
In this case, since the coefficient of x^2 is negative, the parabola opens downwards, indicating that the vertex represents the maximum value.
Hence, the maximum value of f(x) = -0.25x^2 + 4x - 18 is -2, which occurs when x = 8.
Find the minimum or maximum value of f(x)=−0.25x2+4x−18.
recall that the vertex of the parabola
ax^2+bx+c
is at x = -b/2a
So, your maximum is at x = 4/.5 = 8
now just find f(8)