Quadratic Equations

Zero Product Property

When solving quadratics, make one side equal zero, then determine x-values balance the equation to 0.

Taking Square Roots

Isolate x², then square root it. Be sure to simplify and give both the positive and negative answer, if applicable.

Standard Form for Quadratics

ax² + bx + c = 0

Next step for the equation: (x-4)² = 16

Square both sides.

Quadratic Formula

-b+-sqrt(b²-4ac)/2a

Which method is best for the following equation?: 8x²-4x=0

Zero product property (find the GCF)

When completing the square, what should be done to the x² coefficient?

It should be divided out on both sides so x²’s coefficient is one.

Which method is best for the following equation and why?: 3x²+5x-1=0

Quadratic formula: Can’t be neatly factored and has a non-whole “magic constant”.

Which factoring method is best for this equation and why?: (2x+1)²=25

Square rooting (inverse operations) as x² is isolated (in the binomial!)

What are the roots?: -(6x+1)(x+1)>0

-1/6 and -1 [ (6x+1) = 0 is -1/6. ]

Discriminant

Values inside the square root of the quadratic formula that determine the amount of real solutions.

Real Solutions when Discriminant is less than 0

No real solutions.

Real solutions when the discriminant is more than 0

Two

Real solutions when the discriminant is 0

1

Variable used for Interval Notation

x OR y

Magic Constant Formula

(b/2)²

Magic Constant Number Used

Bx