Advantage of rational exponents over the radical sign.

1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following
tasks:

a) Solve by factoring.

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b) Solve by completing the square.

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c) Solve by using the quadratic formula.

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2) For the function y = x2 - 4x - 5, perform the following tasks:

a) Put the function in the form y = a(x - h) 2 + k.

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b) What is the equation for the line of symmetry for the graph of this
function?

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c) Graph the function using the equation in part a. Explain why it is
not necessary to plot points to graph when using y = a (x – h)2 + k.

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d) In your own words, describe how this graph compares to the graph of
y = x2?

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3) Suppose a baseball is shot up from the ground straight up with an
initial velocity of 32 feet per second. A function can be created by
expressing distance above the ground, s, as a function of time, t. This
function is s = -16t2 + v0t + s0

16 represents 1/2g, the gravitational pull due to gravity (measured in
feet per second2).

v0 is the initial velocity (how hard do you throw the object, measured
in feet per second).

s0 is the initial distance above ground (in feet). If you are standing
on the ground, then s0 = 0.

a) What is the function that describes this problem?

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b) The ball will be how high above the ground after 1 second?

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c) How long will it take to hit the ground?

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d) What is the maximum height of the ball? What time will the maximum
height be attained?

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4) John has 300 feet of lumber to frame a rectangular patio (the
perimeter of a rectangle is 2 times length plus 2 times width). He wants
to maximize the area of his patio (area of a rectangle is length times
width). What should the dimensions of the patio be, and show how the
maximum area of the patio is calculated from the algebraic equation.

Show clearly the algebraic steps which prove your dimensions are the
maximum area which can be obtained. Use the vertex form to find the
maximum area.

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