Download Completing the square

1)
How do you know if a quadratic equation will have one, two, or no
solutions?
The standard form of a quadratic equation is:
ax2+bx+c=0 and If:
b2-4ac > 0 then the equation has 2 real solutions
b2-4ac = 0 then the equation has 1 real solutions
b2-4ac < 0 then the equation has 0 real solutions
( d = b2-4ac is the discriminant of the equation )

How do you find a quadratic equation if you are only given the solution?
If  and  are the solutions of a quadratic equation
You can write the factored form of the equation as:
(x-)(x-) = 0
 Is it possible to have different quadratic equations with the same
solution? Explain.
Yes, that happens when an equation is multiplied by a number.
For example: if you multiply the equation: x2- 4=0 by 2 we have:
2x2-8=0.
And the equations x2- 4=0 and 2x2-8=0 have the same solutions (2 and -2)
 Provide your classmate’s with one or two solutions with which they
must create a quadratic equation.
Create a quadratic equation with the solutions: 3 and -5
Answer:
(x-3)(x+5)=0 (factored form)
Or x2+2x-15=0 (standard form)
Quadratic equations can be solved by graphing, using the quadratic
formula, completing the square, and factoring.
2)
 What are the pros and cons of each of these methods?
Graphing:
Pros: You don´t have to solve equations, you find the solutions checking
the graph (solutions are the x-intercepts )
Cons: Is not an exact method, it works fine if the solutions are integer
numbers.
Quadratic formula:
Pros: Always gives you the exact solutions to the problem (2 real solutions,
1 real solution or 2 complex solutions) you always perform the same
operations.
Cons: When the solutions are integers this method can be longer than the
rest of the methods.
Completing the square
Pros: It´s a good method if the process of completing the square is not
complicated.
Cons: If the coefficients are rational or irrational this method can be longer
than the rest of the methods
Factoring:
Pros: When the solutions are integers this method can be shorter than the
rest of the methods
Cons: If the solutions are not exact or not real this method is not short and
surely using the quadratic formula you will know the answers sooner
 When might each method be most appropriate?
If the equations has integer coefficients try to use the factoring method, or
completing the square, If you don´t find real solutions use the quadratic
formula.
If you have the graph of the equation (or it´s easy to do it) use it to try to
find the solutions. If solutions are not exact use another method
 Which method do you prefer? Why?
I prefer the quadratic formula because solutions are exact and we always
perform the same operations, also computing the discriminant (b2-4ac) we
know the number of real solutions