Final answer:
To find the maximum or minimum value of the function f(x) = 12x² + 4x − 12, we can find the vertex of the parabola. The vertex represents the minimum value of the function in this case.
Step-by-step explanation:
To find the maximum or minimum value of the function f(x) = 12x² + 4x − 12, we can use the concept of the vertex of a parabola. The vertex is the highest or lowest point of a parabola, which corresponds to the maximum or minimum value of the function.
The general form of a quadratic function is f(x) = ax² + bx + c. To find the vertex, we can use the formula x = -b / (2a). In this case, a = 12 and b = 4.
Substituting these values into the formula, we get:
x = -4 / (2 * 12) = -1/6.
Substituting this value back into the original function, we can find the y-coordinate of the vertex:
f(-1/6) = 12(-1/6)² + 4(-1/6) - 12 = -5.
Since the leading coefficient (a) is positive, the parabola opens upwards, which means the vertex represents the minimum value of the function. Therefore, the minimum value of the function f(x) = 12x² + 4x − 12 is -5.
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