Two scientists are running experiments on the same type of friction in different control groups. the results are shown in the graph using the functions f(x) and g(x):
graph of two functions in quadrant 1, f of x equals 2 times x plus 3 and g of x equals one tenth times 3 to the x power
which statement best describes the graph of f(x) and g(x)?
a)the graphs will both have their y-intercept equal to 3.
b)the graphs will both have their y-intercept equal to 4.
c) the graph of f(x) will eventually exceed the graph of g(x).
d)the graph of g(x) will eventually exceed the graph of f(x).

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solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like: