The functions f(x) = (x + 1)2 − 2 and g(x) = −(x − 2)2 + 1 have been rewritten using the completing-the-square method. apply your knowledge of functions in vertex form to determine if the vertex for each function is a minimum or a maximum and explain your reasoning.

Step-by-step explanation:

A positive parabola is one that has a + sign out front or no sign at all (and the positive is understood).  A positive parabola opens like a cup with a bottom.  Therefore, the positive parabola has a min value.  A negative parabola opens upside down, like a mountain with a peak.  Therefore, the negative parabola has a max value.

1.3 million hoops i believe

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb