# Functions, Zeros And Application

Given f(x) = ex2 + fx + g, where e, f, and g are real numbers,

(a) Find the zeros of the function in terms of e, f, and g.

(b) Under what condition would the zeros of the given function be two distinct real values?

(c) Determine the x-coordinate (the x-value) of the point that would represent the minimum or the maximum of the graph of the function by taking the average (mean value) of the zeros of the function found in Part (a).

(d) Under what condition would the graph of the function have a maximum, not a minimum, with the x-value obtained in Part (c)?

(e) Draw the graph of a function, with numerical coefficients of your choice, to represent your thought on what you stated in Part (d).

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(a) f(x) = ex2 + fx + g

f(x) = ex2 + fx + g = (x - x1) (x-x2) where x1 and x2 are the solution to the quadratic formula f(x)

Using the quadratic formula the solution to f(x) ...

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1) Solve the following equations.

a)

Answer:

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b) .

Answer:

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c) .

Answer:

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2) Is an identity (true for all values of x)?

Answer:

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3) For the equation , perform the following:

a) Solve for all values of x that satisfies the equation.

Answer:

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b) Graph the functions and on the same graph (by plotting points if necessary). Show the points of intersection of these two graphs.

Graph

c) How does the graph relate to part a?

Answer:

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Answer:

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5) Suppose you travel north for 35 kilometers then travel east 65 kilometers. How far are you from your starting point? North and east can be considered the directions of the y- and x-axis respectively.

Answer:

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6) The volume of a cube is given by V = s3. Find the length of a side of a cube if the Volume is 729 cm3.

Answer:

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