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).

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

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).

To determine which function has the least minimum value and its coordinates, we need to find the vertex of each function and compare the y-values of the vertex points.

For Function 1:
The given function is f(x) = 4x^2 + 8x + 1.
To find the vertex of a quadratic function in the form of f(x) = ax^2 + bx + c, we can use the formula x = -b / 2a.
In this case, a = 4 and b = 8.

x = -b / 2a
x = -8 / 2(4)
x = -8 / 8
x = -1

To find the y-coordinate, substitute the x-coordinate back into the function.
f(-1) = 4(-1)^2 + 8(-1) + 1
f(-1) = 4 + (-8) + 1
f(-1) = -3

Therefore, the vertex of Function 1 is (-1, -3).

For Function 2:
The given function is:
x -2 -1 0 1
g(x) 2 0 2 8

To find the vertex of a quadratic function, we look for the minimum or maximum point. In this case, since the vertex is at the minimum point, we need to find the lowest y-value in the table.

The lowest y-value in the table is 0, which occurs at x = -1.

Therefore, the vertex of Function 2 is (-1, 0).

Comparing the y-values of the vertex points, we can conclude that Function 1 has the least minimum value since -3 is smaller than 0.

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

To determine which function has the least minimum value and its coordinates, we need to find the vertex of each quadratic function.

Function 1: f(x) = 4x^2 + 8x + 1

The vertex of a quadratic function in the form f(x) = ax^2 + bx + c can be found using the formula x = -b / (2a).

For Function 1, a = 4 and b = 8. Plugging these values into the formula, we get:

x = -8 / (2 * 4)
x = -8 / 8
x = -1

To find the y-coordinate of the vertex, we substitute this value of x back into the function:

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

Therefore, the vertex of Function 1 is (-1, -3).

Now let's examine Function 2:

x -2 -1 0 1
g(x) 2 0 2 8

From the given table, we can see that the minimum value of Function 2 occurs at x = -1, and the corresponding y-coordinate is 0.

Therefore, the vertex of Function 2 is (-1, 0).

Comparing the vertices of both functions, we can conclude that Function 1 has the least minimum value, and its coordinates are (-1, -3).