Determine whether each function has a maximum or minimum value. Then find the value

8. Y=-x^2+4x-4

For f (x) = ax²+bx+c

if a is positive, then it is concave up and the verx is minimum

if a is ngative then it is concave down and vertex is maximum

hack: in form f (x) = ax²+bx+c, the x value of vertex is - b/2a

to find y value, just subsitutte that value for x in f (x)

so

y=-1x²+4x-4

negative, so vertx is max

x value of vertex is - 4 / (2*-1) = - 4/-2=2

find f (2) or subsitute 2 for x

y=-1 (2) ²+4 (2) - 4

y=-1 (4) + 8-4

y=-4+4

y=0

maximum is 0

A is answer

Y = - x^2+4x-4

Standard form is

Y=ax^2+bx+c

here cofficient of a is negative so this is downward parabola.

so it will have maximum value at its vertex

h=-b/2a

h = - 4/2 (-1)

h=2

put h in equation y = - x^2+4x-4

that will be other vertex K

k = - (2) ^2+4*2-4

k=-4+8-4

k=0

vertex (h, k) = (2,0)

y = (x-2) ^2+0

maximum value is k which is 0