Question

Two quadratic functions are shown.

Function 1:
f(x) = 4x2 + 8x + 1

Function 2:
x g(x)
−2 2
−1 0
0 2
1 8
Which function has the least minimum value and what are its coordinates? (5 points)

Group of answer choices

Function 1 has the least minimum value and its coordinates are (−1, −3).

Function 1 has the least minimum value and its coordinates are (0, 1).

Function 2 has the least minimum value and its coordinates are (−1, 0).

Function 2 has the least minimum value and its coordinates are (0, 2).

Answer 1

Option (1) is the correct option.

Explanation:

Function 1,

f(x) = 4x² + 8x + 1

= 4(x² + 2x) + 1

= 4(x² + 2x + 1 - 1) + 1

= 4(x² + 2x + 1) - 4 + 1

f(x) = 4(x + 1)² - 3

This graph opens up with the vertex or minimum point at (-1, -3)

So, the minimum value of the function is (-3) at x = -1.

Function (2)

From the given table minimum value of the function is 0 at x = -1 or minimum point as (-1, 0)

Therefore, Function 1 has the least minimum value and its coordinates are (-1, -3)

Option (1) is the correct option.