ALGEBRA

wo quadratic functions are shown.

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

Function 2:
x -2 -1 0 1
g(x) 2 0 2 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).

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  1. function1 is a parabola with a vertex of (-1,-3) so its minimum is -3
    since function2 shows a minimum value of 0

    the first statement is true
    min value of -3 at the point (-1,-3).

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  2. the minimum of function 2 is 0 at (-1,0)

    for the first function 1

    y = 4 x^2 + 8 x + 1

    4 x^2 + 8 x = y - 1

    x^2 + 2 x = (1/4) y - 1/4

    x^2 + 2 x + 1 = (1/4)y + 3/4

    (x+1)^1 = (1/4) (y+3)
    so vertex at (-1, -3)

    SO A

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