Question

(09.01 MC)

Two quadratic functions are shown.
Function 2:
Function 1:
f(x) = 2x2 - 8x + 1
|x
g(x)
1
17
Which function has the least minimum value and what are its coordinates? (5 points)
Function 1 has the least minimum value and its coordinates are (0, 1).
Function 1 has the least minimum value and its coordinates are (2. - 7).
Function 2 has the least minimum value and its coordinates are (0,2).
Function 2 has the least minimum value and its coordinates are (-1.-3).

Answer 1

Function 1 has the least minimum value and its coordinates are (2. - 7).

Explanation:

The first function is

`f(x)=2x^(2) -8x+1`

The second function is

x g(x)

-2 2

-1 -3

0 2

1 17

The vertex has coordinates of
`V(h,k)`, where
`h=-(b)/(2a)` and
`k=f(h)`.

Let's find the vertex for the first function where
`a=2` and
`b=-8`.

`h=-(-8)/(2(2))=2`

`k=f(2)=2(2)^(2) -8(2)+1=8-16+1=-8+1=-7`

Therefore, the vertex of the first function is at
`(2,-7)`.

Now, the minimum value of the second function can be deducted from its table, which is
`(-1,-3)`.

Therefore,
`f(x)` has -7 as minimum value and
`g(x)` has -3 as minimum vale.

So, the right answer is B, because -7 is less than -3.