Explore BrainMass

How do you find the solution to a quadratic equation by factoring, completing the square and using the quadratic formula?

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
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).
· 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?
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.


Solution Preview

Following is the text part of the solution. Please see the attached file for complete solution. Equations, diagrams, graphs and special characters will not appear correctly here. Thank you for using Brainmass.

IP Unit 2
Section Number:


· Identify the document by typing your full name and section number next to the yellow text.
· Rename the file by adding your last name to current file name (e.g., "u2ip_lastname.doc").
· Type your answers next to the yellow text.
· To show your work, you will need to include
o the algebra used to compute the solution to any equations
o the formula with substituted values.
o the final calculated answer with units.
· To utilize the scientific calculator on your computer, do the following:
o Open the calculator (if it is not in the accessories folder, then select Run from the Start menu)
o Select View from the drop down menu
o Select Scientific to utilize the calculator.
o Note that x^y computes any number to any power (integer, fraction, decimal).

Please submit your assignment.

1) Using the quadratic equation x2 - 3x + 2 = 0, perform the following tasks:
a) Solve by factoring.
Show work in this space.
x2 - 3x + 2 = (x - 1)(x - 2)
(x - 1)(x - 2) = 0
(x - 1) = 0 or (x - 2) = 0
X = 1 or X = 2

b) Solve by completing the square.
Show work in this space.
x2 - 3x + 2 = ...

Solution Summary

A quadratic equation is solved by three different methods: Factoring, Completing the square and using the quadratic formula. Solution also includes Graphing an equation. Finally two word problems involving quadratic equations are solved. This solution is provided as an attached Word document.