Question

What is the minimum value for g(x)=x2−10x+16?
Enter your answer in the box.

y =

Answer 1

Just took the test the answer is -9!

Explanation:

Answer 2

`y=-9`

Explanation:

The given function is

`g(x)=x^(2) -10x+16`

As you can notice, this is a quadratic function. That means its graphic behaviour is a parabola.

So, a parabola has a minimum or maximum, in either case, that point is the vertex. That means we need to find the vertex of this function and its vertical coordinate will be the minimum.

The vertex has coordinates of
`V(h,k)`, where
`h=-(b)/(2a)`, and
`a=1, b=-10, c=16`.

Replacing each value, we have

`h=-(b)/(2a)=-(-10)/(2(1))=5`

The other coordinate is defined as
`k=f(h)`, that is, we need to replace the number 5 in the function to obtain k

`g(x)=x^(2) -10x+16\\g(5)=(5)^(2) -10(5)+16=25-50+16=-9`

Therefore, the minimum is at
`y=-9`