3.3 Completing the Square 23-24

Front

What is a Perfect Square Trinomial?

Back

A Perfect Square Trinomial is a quadratic expression that can be written in the form (a + b)² = a² + 2ab + b².

Front

How do you create a Perfect Square Trinomial from x² + 6x?

Back

To create a Perfect Square Trinomial, add (6/2)² = 9 to get x² + 6x + 9 = (x + 3)².

Front

What is the first step in completing the square for the equation 7x² - 14x - 56 = 0?

Back

First, move the constant term to the other side: 7x² - 14x = 56.

Front

How do you isolate the x² term in the equation x² = 9 - 4x?

Back

You need 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

What are the solutions to the equation a² - 2a - 35 = 0 after completing the square?

Back

The solutions are a = -5 and a = 7.

Front

What does it mean to complete the square?

Back

Completing the square involves rewriting a quadratic equation in the form (x + p)² = q to make it easier to solve.

Front

How do you solve (2x - 1)² = 49?

Back

Take the square root of both sides: 2x - 1 = ±7, leading to x = 4 and x = -3.

Front

What is the significance of the term (b/2)² in completing the square?

Back

It is the value added to both sides of the equation to form a perfect square trinomial.

Front

What is the vertex form of a quadratic equation?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.