Page 3: Practical Applications

This page applies the completing the square method to find the turning point of the quadratic function y = 2x² + 16x + 26, demonstrating practical applications in graphing.

Example: Converting 2x² + 16x + 26 into 2(x+4)² - 6

Highlight: The turning point (-4, -6) is essential for sketching the quadratic graph accurately.

Definition: The turning point represents the vertex of the parabola, where the function changes from increasing to decreasing or vice versa.

Page 1: Basic Completing the Square

This page demonstrates the fundamental process of completing the square method for quadratic equations using a straightforward example with x² + 8x + 12. The method systematically transforms the quadratic expression into a perfect square form.

Example: Converting x² + 8x + 12 into (x+4)² - 4

Definition: Completing the square involves rewriting a quadratic expression in the form (x + p)² + q, where p and q are constants.

Highlight: The turning point can be directly read from the completed square form as (-4, -4).

Vocabulary: The term "perfect square" refers to an expression that can be written as a binomial squared.