The derivation for the equation of a parabola with a vertex at the origin is started below. = StartRoot (x minus 0) squared + (y minus p) squared EndRoot = StartRoot (x minus x) squared + (y minus (negative p)) squared EndRoot (x)2 + (y – p)2 = (0)2 + (y + p)2 x2 + y2 – 2py + p2 = y2 + 2py + p2 If the equation is further simplified, which equation for a parabola does it become? x2 = 4py x2 = 2y2 + 2p2 y2 = 4px y2 = 4py

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.

Write each fraction as an equivalent fraction with a denominator of 120then write the original fractions in order from samllest to largest

A. plot the data for the functions f(x) and g(x) on a grid and connect the points. x -2 -1 0 1 2 f(x) 1/9 1/3 1 3 9 x -2 -1 0 1 2 g(x) -4 -2 0 2 4 b. which function could be described as exponential and which as linear? explain. c. if the functions continue with the same pattern, will the function values ever be equal? if so, give estimates for the value of x that will make the function values equals. if not, explain why the function values will never be equal.