Solving Quadratic Equations by Completing the Square (Grade 9 Module: M9AL Ia-b-1)

Vocabulary flashcards covering key concepts from solving quadratic equations by completing the square.

Completing the square

A method for solving quadratic equations by transforming a quadratic into a perfect square trinomial, typically by adding a constant to both sides.

Perfect square trinomial

A trinomial that can be written as a squared binomial, such as (x ± a)^2; its first and last terms are perfect squares and the middle term equals twice the product of their roots.

Incomplete square

A quadratic expression that is not yet a perfect square and needs an added constant to become one.

Completed square

The resulting expression after adding the necessary constant to form a perfect square, e.g., x^2 + 6x + 9 = (x + 3)^2.

Square root

A number that, when squared, gives the original number; used to solve equations after isolating a perfect square.

Coefficient of x (linear coefficient)

The number multiplying x in a term; in ax^2 + bx + c, b is the coefficient of x.

Quadratic equation

An equation of the form ax^2 + bx + c = 0 with a ≠ 0.

Solution set

The set of all values of the unknown that satisfy the equation, often written {x1, x2} for a quadratic.

Root

A solution of a polynomial equation; a value of x that makes the equation true.

Factored form

An expression written as a product of factors, such as (x + 4)^2 for a perfect square trinomial.

Binomial

A polynomial expression with two terms, such as x + 4.

Trinomial

A polynomial expression with three terms, such as x^2 + 8x + 16.

Constant term

The term in a polynomial that does not contain a variable (the numerical term).

Middle term

In a trinomial ax^2 + bx + c, the middle term is the linear term bx.

Square of a binomial

The expansion of (x ± a)^2 which yields x^2 ± 2ax + a^2.

Term to complete the square (for x^2 + bx)

The constant to add to x^2 + bx to form a perfect square, equal to (b/2)^2.