Answer:
Minimum value
Explanation:
Step 1: Identify the form of f(x) = 4x^2 - 9x - 5:
The equation 4x^2 - 9x - 5 is in the standard form of a quadratic function, whose general equation is given by;
f(x) = ax^2 + bx + c.
Thus, 4 is our a value, -9 is our b value, and -5 is our c value.
Step 2: Find the x-coordinate of the vertex:
We can use the following formula to find the x-value of the vertex:
x = -b / 2a
Thus, we can plug in -9 for b and 4 for a:
x = -(-9) / 2(4)
x = 9/8
Thus, the x-coordinate of the vertex is 9/8
Step 3: Find the y-coordinate of the vertex:
The minimum or maximum value refers to the y-coordinate of the vertex.
We can plug in the x-coordinate we just found to find the y-coordinate of the vertex.
If it's positive, the function has a maximum value.
If it's negative, the function has a minimum value.
Plugging in 9/8 for x in f(x) = 4x^2 - 9x - 5:
f(9/8) = 4(9/8)^2 - 9(9/8) - 5
f(9/8) = 4(81/64) - 81/8 - 5
f(9/8) = 81/16 - 121/8
f(9/8) = -161/16
Thus, the function has a minimum value.