Answer:
−10x+3
Step-by-step explanation:
y=8(x^2 + 4x + 4) +17 + -32
Simplify:
y = 8(x^2 + 4x + 4) + 15
Use distributive property:
y = 8x^2 + 32x +32 - 15
Simplify:
y = 8x^2 + 32x +17
Complete the square using form ax^2+bx+c:
a = 8, b = 32, c = 17
vertex form = a(x+d)^2+e
d = b/2a and e = c-b^2/4a
d = 32/2*8 = 32/16 = 2
e = 17 - 32^2/4*8 = 17-1024/32 = 17-32 = -15
Vertex form = y = 8(x+2)^2 + -15
4! Or 22 :))))))))))))))))))) hope I got it right!
Let the length of the side of the 4 small squares be = x.
The formula for the volume of the box will be
height * width * length
V = x ( 9 - 2x)^2
V = 81x - 36x^2 + 4x^3
finding the derivative:-
dV / d x = 12x^2 - 72x + 81
THis equals 0 for a maximum / minimum value
12x^2 - 72x + 81 = 0
3(4x^2 - 24x + 27) = 0
x = 4.5 , 1.5
Use second derivative to find maxm and minm:-
d^2V / dx^2 = 24x - 72
when x = 1.5 this is negative and when x = 4.5 this is positive
so x = 1.5 gives a maximum value for V
V = 1.5(9- 2(1-5))^2 = 54
Largest possible volume of the box is 54 cm^3 Answer