Question

Please help I will give a medal

Two 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).

Answer 1

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

Explanation:

Any quadratic function can be written in the form:

`f(x)=ax^(2) +bx+c`

The x of the vertex can be fiund by x=-b÷2a

Function 1 is given by:
`f(x)=4x^(2) +8x+1`

Comparing the quadratic equations we have a=4,b=8,c=1.

The x of the vertex is -b÷2a=-8÷2(4)=- 8÷8= -1.

The y of the vertex can be found by substituting x= -1 in the original function and solving for y.

`y=4(-1^(2) )+8(-1)+1=-3`

Vertex of f(x)=(-1,-3)

For function g(x) minimum is at (0,0)

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

Answer 2

Funtion ! 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 minimun 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)