1. We found numbers h and k such that, for every real number
x, ax^2 + bx + c = a(x − h)^2 + k as long as a, b and c are real numbers and a≠0.

(a) What are those numbers h and k in terms of a, b and c?

(b) Now, if a > 0, use the fact that t^2 ≥ 0 for every real number t to conclude ax^2+ bx + c ≥ k for every real number x.

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. release your mouse button when the item is place. if you change your mind, drag the item to the trashcan. click the trashcan to clear all your answers. using the technique in the model above, find the missing segments in this 30°-60°-90° right triangle. ab = 8 bc = 4 cd =

James is playing his favorite game at the arcade. after playing the game 3 times, he has 8 tokens remaining. he initially had 20 tokens, and the game costs the same number of tokens each time. the number tt of tokens james has is a function of gg, the number of games he plays

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria.the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time.create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.