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?

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

The answer is A: Function 1 has the least minimum value and its coordinates are (-1, -3).

Explanation:

Answer 2

Funtion 1 in vertex form is given by...

f(x) = 4x^2 + 8x + 1 = 4(x^2 + 2x + 1/4) = 4(x^2 + 2x + 1 + 1/4 - 1) = 4(x + 1)^2 + 4(-3/4) = 4(x + 1)^2 - 3.

Thus, the least minimum value is (-1, -3).

Also, the least minimum value of function 2 is (-1, 0).
Therefore, function 1 has the least minimum value at (-1, -3).