The vertex of f(x) = 3x^2 + 12x − 8 is (2,28) absolute minimum
<h3>How to determine the vertex?</h3>
The equation is given as:
f(x) = 3x^2 + 12x − 8
Differentiate the function
f'(x) = 6x + 12
Set to 0
6x + 12 = 0
Divide through by 6
x + 2 = 0
Solve for x
x = -2
Substitute x = -2 in f(x) = 3x^2 + 12x − 8
f(2) = 3 *2^2 + 12 *2 − 8
Evaluate
f(2) = 28
This means that the vertex is (2,28)
A quadratic function is represented as:
f(x) =ax^2 + bx + c
When a is positive, then the vertex of the function is an absolute minimum.
This means that f(x) = 3x^2 + 12x − 8 has an absolute minimum vertex because 3 is positive
Read more about quadratic functions at:
brainly.com/question/18797214
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