minimum value
The y-coordinate of the vertex of the quadratic function f(x)=ax^2+bx+c, where a>0
In mathematics, the minimum value is the smallest possible value that a function or set of data can take. This value is also known as the absolute minimum or global minimum, depending on the context in which it is used.
To find the minimum value of a function, you need to first determine the domain of the function, which is the set of all possible inputs. You then need to evaluate the function at different points within this domain and determine which point produces the smallest output value.
For example, let’s say we have the function f(x) = 2x² + 4x – 3. To find the minimum value of this function, we take the derivative (f'(x)) and set it equal to zero:
f'(x) = 4x + 4 = 0
x = -1
Next, we plug this value back into the original function to find the minimum value:
f(-1) = 2(-1)² + 4(-1) – 3 = -5
Therefore, the minimum value of the function f(x) = 2x² + 4x – 3 is -5, which occurs at the point (-1, -5).
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