Completing the Square

Front

What is the first step in completing the square for a quadratic equation?

Back

Rearrange the equation to isolate the constant term on one side.

Front

How do you find the value to complete the square for the expression x^2 + bx?

Back

Divide b by 2 and square the result.

Front

What is the completed square form of x^2 + 6x?

Back

(x + 3)^2 - 9.

Front

What is a perfect square trinomial?

Back

A trinomial that can be expressed as the square of a binomial, e.g., (x + a)^2 = x^2 + 2ax + a^2.

Front

How do you convert x^2 + 12x into completed square form?

Back

x^2 + 12x + 36 = (x + 6)^2.

Front

What does the term 'completing the square' refer to?

Back

A method used to convert a quadratic equation into a perfect square trinomial.

Front

What is the significance of completing the square in solving quadratic equations?

Back

It allows for easier solving and graphing of quadratic functions.

Front

What is the completed square form of x^2 - 18x + 81?

Back

(x - 9)^2.

Front

How do you check if a trinomial is a perfect square?

Back

Verify if it can be expressed as (x + a)^2 or (x - a)^2.

Front

What is the vertex form of a quadratic equation?

Back

y = a(x - h)^2 + k, where (h, k) is the vertex.