Question

Two quadratic functions are shown.

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

Function 2:


−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

So I think the question is basically asking for the minimum y value you could get from the functions.
For the first function,

`y=4 x^(2) +8x+1`
to find the minimum y. (Use x=-b/2a to find its vertex)
so in this case a=4 b=8
x=-8/2(4)=-1 the the minimum value will have -1 as its x coordinates,

`y=4(-1)^2+8(-1)+1=4-8+1=-3` plug in x=-1 to find y.
(-1,-3) for minimum value for the first function
For the second function,
(-1,0) is the vertex of the function, which is the minimum of the function.

compare the first function with y=-3 and second function y=0.
The first function will have the least minimum value and the coordinates are (-1,-3).