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Quadratic Equations and Maximum and Minimum Values

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Note that x^y computes any number to any power (integer, fraction, decimal).

1)Using the quadratic equation x2 - 3x + 2 = 0, perform the following tasks:

a)Solve by factoring.

b)Solve by completing the square.

c)Solve by using the quadratic formula.

2)For the function y = x2 - 6x + 8, perform the following tasks:

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

b)What is the line of symmetry?

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.
Show graph here.

Explanation of graphing.

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

3)Suppose you throw a baseball straight up at a 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 ½g, the gravitational pull due to gravity (measured in feet per second 2).

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

s 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?

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

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

d)What is the maximum height of the ball?

4)Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her 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.

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