Question

What is the maximum value of the function f(x)=-x^2+6x+1 (enter an exact number) rotate image to see the problem

Answer 1

`10`

Explanation:

`f(x)=-x^2+6x+1`

x coordinate:

`(-b)/(2a)`

`a=-1\\b=6`

`(-6)/(2(-1)) \\(-6)/(-2)\\ =3`

y-coordinate:

`f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10`

Answer 2

10

Explanation:

f(x)=-x^2+6x+1

This is a parabola that opens downward( the - coefficient of x^2)

The maximumx is at the vertex

The x coordinate is at

-b/2a where ax^2 + bx +c a =-1 b=6 c=1

-6/(2*-1)

-6/-2 = 3

The x coordinate of the vertex is 3

f(3) = - (3)^2 +6(3)=1

= -9+18+1

= 10

The vertex is ( 3,10)

The maximum value is 10