Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2?
g(x) = –9(x2 + 2x + 1) – 7
g(x) = 4(x2 – 6x + 9) + 1
g(x) = –3(x2 – 8x + 16) – 6
g(x) = 8(x2 – 6x + 9) – 5

The last choice is the one you want

Step-by-step explanation:

First of all, a parabola has a minimum value if it is a positive parabola, one that opens upward.  The first and the third parabolas are negative so they open upside down.  That leaves us with choices 2 and 4.  We find the side to side and up or down movement by finishing the completion of the square that has already been started for us.  Do this by factoring what's inside the parenthesis into a perfect square binomial.  

The second one factored becomes:

which reflects a shift to the right 3 and up 1.  Not what we are asked to find.

The fourth one factored becomes:

which reflects a shift to the right 3 and down 5.  That's what we want!

g(x) = 8(x2 – 6x + 9) – 5

Step-by-step explanation:

A function with a form (x - a)^2 - b where a and b are some constants are a transformation to the right and down from the parent function, f(x) = x^2.  Then,  option:

g(x) = 4(x2 – 6x + 9) + 1 = 4(x - 3)^2 + 1

is discarded

The vertex form of a quadratic equation is f(x) = c*(x - h)^2 + k, where c, h and k are all constant, and point (h,k) is the vertex of the quadratic function. If c > 0, then the vertex is a minimum and if c < 0 then the vertex is a maximum. Therefore, options:    

g(x) = –9(x2 + 2x + 1) – 7 = -9(x + 1)^2 - 7

g(x) = –3(x2 – 8x + 16) – 6 = -3(x - 4)^2 - 6

are dicarded

In consequence, the correct option is:

g(x) = 8(x2 – 6x + 9) – 5 = 8(x - 3)^2 - 5

mr. flanders’ class sold 47 doughnuts and   mr. rodriquez’s class sold 38 cartons of milk

step-by-step explanation:

let x be the number of doughnuts sold by mr. flanders’ class and y be the number of cartons sold by mr. rodriquez’s class.

1. together, the classes sold 85 items, then

x+y=85.

2. both classes earn earned $104.49 for their school. if doughnuts were sold for $1.35 each, then x doughnuts costed $1.35x. if cartons of milk were sold for $1.08 each, then y cartons costed $1.08y. hence,

1.35x+1.08y=104.49.

3. solve the system of two equations:

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