Identify the coordinates of the vertex of f(x) = 3x2 + 12x − 8, and identify whether it is an absolute minimum or absolute maxim

Question

2 years ago

5

um. (2, 28), absolute minimum Correct Answer (−2, −20), absolute minimum Incorrect Response (−2, −20), absolute maximum (2, 28), absolute maximum

1 answer:

DaniilM [7] · Answer 1 · 2023-09-23T21:05:51+03:00

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

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