Assignment #1 - Completing the Square

Front

What is 'Completing the Square'?

Back

Completing the Square is a method used to solve quadratic equations by rewriting them in the form (x - p)² = q, making it easier to find the roots.

Front

What is a perfect square trinomial?

Back

A perfect square trinomial is an expression that can be factored into the square of a binomial, such as x² - 6x + 9 = (x - 3)².

Front

How do you complete the square for the equation x² + 6x = 5?

Back

1. Move 5 to the other side: x² + 6x - 5 = 0. 2. Take half of 6 (which is 3), square it (9), and add to both sides: (x + 3)² = 14.

Front

What is the value of 'c' in the expression x² + 6x + c to complete the square?

Back

c = 9, because (x + 3)² = x² + 6x + 9.

Front

What does it mean to factor a quadratic expression?

Back

Factoring a quadratic expression means rewriting it as a product of its linear factors, such as x² - 4x + 4 = (x - 2)².

Front

What is the first step in completing the square for x² = 9 - 4x?

Back

The first step is to move -4x to the other side, resulting in x² + 4x = 9.

Front

What is the formula for completing the square?

Back

The formula is: x² + bx = (x + b/2)² - (b/2)².

Front

How do you identify a perfect square trinomial?

Back

A trinomial is a perfect square if it can be expressed as (a ± b)², where a² is the first term, 2ab is the middle term, and b² is the last term.

Front

What is the significance of the vertex form of a quadratic equation?

Back

The vertex form, y = a(x - h)² + k, allows you to easily identify the vertex (h, k) of the parabola.

Front

What is the relationship between the coefficients and the roots of a quadratic equation?

Back

For a quadratic equation ax² + bx + c = 0, the sum of the roots is -b/a and the product of the roots is c/a.