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).

Option (1) is the correct option.

Step-by-step 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.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

answer: -1

step-by-step explanation: