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Two Friends: Linear and Quadratic Equations

You know a lot about linear and quadratic equations...but do you actually know about them?

Consider linear equation Ax+By+C = 0. What is the effect if...

  • The value of A is doubled (or multiplied by some constant k)?
  • The value of B is doubled (or multiplied by some constant k)?
  • The value of C is doubled (or multiplied by some constant k)?
  • The value of A is multiplied by -1?
  • The value of B is multiplied by -1?
  • The value of C is multiplied by -1?
Now, consider the quadratic equation Ax2+Bx+C = 0. What is the effect if...
  • The value of A is doubled (or multiplied by some constant k)?
  • The value of B is doubled (or multiplied by some constant k)?
  • The value of C is doubled (or multiplied by some constant k)?
  • The value of A is multiplied by -1?
  • The value of B is multiplied by -1?
  • The value of C is multiplied by -1?
How did you do with this impromptu quiz....If nothing else, after exploring it, you now know even more about linear and quadratic equations.

 


Hint: For linear equation, a good start is to shift it into standard form y = .... and then graph it using the parameters A, B, and C.

Basically ther same approach is a good start for the quadratic case as well...

 


Solution Commentary: No solutions provided, as you can explore and argue about this on your own....but, I will say that with each change, something happens....that can be explained mathematically!