to SR from our first session Sunday 3/4/07 ... Written by Steve Bergen, bergen@chapin.edu

Notes on Quadratics

• Quadratics have 0 or 1 or 2 solutions
• when you have the quadratic in standard form, you can identify A, B and C and then do a quick calculation to generate the DISCRIMINANT which is B² - 4AC ... be very careful with + and - in working with A, B and C
• If the discriminant is 0, this means there is just one solution and the parabola touches the X - axis just once
• If the discriminant > 0, this means that there are two solutions but they may be easy or difficult to figure out ... but knowing that there are two is helpful and it means that the parabola hits the x-axis twice
• If the discriminant < 0, this means that there are ZERO solutions and it means that the parabola never hits the x-axis
• If the discriminant is a perfect square (e.g. 1,4,9,16,25) then this means that the quadratic is factorable since the SQUARE ROOT of the discriminant is going to be used in the quadratic formula

Useful Links for More Info

• Quadratic Equation Solver ... click here
• Click here for the quadratic formula and the quadratic solver where you can plug in the values of A, B and C
• Click here for some examples done step by step with the quadratic formula
• Click here for "where the quadratic formula comes from" ... this is very challenging!
• Click here for an overview of parabolas
• Click here for a qudratic formula rap tune ;-)
• Click here here for math poems including the Quadratic Formula set to "Mary had a little lamb"

Useful Sites: ThinkQuest | Knoxville TN | Online Tools Univ Vienna | NLVM Utah | Thinking Blocks | Shodor NC

Some problems sent 3/19/07

1. I am thinking of a number. When you square it and then multiply by 4 you get 100. What's my number?
2. I am thinking of a number. When you square it and add 10, you get 6. What's my number?
3. Isiah Thomas drops a basketball from 300 feet above the court. Approximately how many seconds does it take to hit the ground?

Answer below

1. I am thinking of a number. When you square it and then multiply by 4 you get 100. What's my number?

    SOLUTION
    
    Let X = the number
    then you get X2  for x-squared
    and 
    4x2  for 4x-squared
    so 4 x2  = 100
    and so 
    x^2 = 25
    and so 
    x = 5 or x = -5 (two answers)
    
    remember that when x2  = a positive number there are TWO solutions
    in this case +5 and -5
    
    
    

2. I am thinking of a number. When you square it and add 10, you get 6. What's my number?

    SOLUTION
    
    Let X = the number
    then you get x2  +10 = 6
    subtracting 10 from each side gives
    x2  = -4
    
    but no number that we know (so far) when squared = a negative number
    so there are no solutions!
    
    
   
    
    

3. Isiah Thomas drops a basketball from 300 feet above the court. Approximately how many seconds does it take to hit the ground?

    SOLUTION
    
    our universal formula is that
    
    Height = Initial height - 16 T2 
   
   H = initial height - 16 T2 
   
   so in this case
   
   H = 300 - 16 T2 
   
   and we want to know when H will equal ZERO
   
   0 = 300 - 16 T2 
   
   or
   
   16 T^2 = 300
   
   t2 = 300/16 = 18.75
   
   so the solution is the square root of 18.75 
   
   T = 4.33 seconds