Determine Whether the Given Quadratic Function Has a Minimum Value $$f ( x ) = 4 x ^ { 2 } + 2 x + 2$$

question 373

Multiple Choice

Determine whether the given quadratic function has a minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
- $$f ( x ) = 4 x ^ { 2 } + 2 x + 2$$

• A) minimum; \(\left( - \frac { 1 } { 4 } , \frac { 7 } { 4 } \right)\)
• B) maximum; \(\left( - \frac { 1 } { 4 } , \frac { 7 } { 4 } \right)\)
• C) minimum; \(\left( \frac { 7 } { 4 } , - \frac { 1 } { 4 } \right)\)
• D) maximum; \(\left( \frac { 7 } { 4 } , - \frac { 1 } { 4 } \right)\)

---

Definitions:

Common Difference

The steady gap found between successive numbers in an arithmetic progression.

Common Ratio

In a geometric sequence, the consistent factor by which each term is multiplied to produce the next term.

Geometric Sequence

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Common Ratio

In a geometric sequence, the constant factor by which each term is multiplied to get the next term.