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

answer: 140

step-by-step explanation:

so just add all then it will be your answer but i am not pretty sur eif it is but hope this i am here to people

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.