Quadratic Equations: Completing the Square in Algebra

Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks:
a) Solve by factoring.
Answer:

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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.
Answer:

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b) What is the line of symmetry?
Answer:

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 to the graph of y = x2?

Answer:

3) Suppose you throw a baseball straight up at a velocity of 64 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?
Answer:
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c) How long will it take to hit the ground?
Answer:
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d) What is the maximum height of the ball? What time will the maximum height be attained?
Answer:

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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.

Answer:

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When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative.
Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx + c.