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.

You invested $5000 between two accounts paying 4% and 9% annual interest, respectively. if the total interest earned for theyear was $350, how much was invested at each rate? $was invested at 4% andwas invested at 9%.

Expresa commuter train leaves downtown sation and travels at a average speed of 55 miles per hour towards the north side sation, which is 50miles away. thirty minutes later, express commuter train #7 leaves north side and travels at a average speed of 35miles per hour towards downtown sation. at the moment the two trains pass each other, how far(in miles) is train #12 from the downtown sation and how long(in minutes) has the #12 train been traveling

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.