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

Answer:

$10$

Step-by-step explanation:

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

x coordinate:

$\frac{-b}{2a}$

$a=-1\\b=6$

$\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3$

y-coordinate:

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

Answer 2

Answer:

10

Step-by-step 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