Page 2: Advanced Completing the Square

This page explores more complex scenarios in factorising and completing the square in quadratics, particularly when dealing with coefficients other than 1. The example works through 2x² + 10x + 8.

Example: Converting 2x² + 10x + 8 into 2$x-2.5$² - 4.5

Highlight: When the x² coefficient isn't 1, factor it out before completing the square.

Definition: The turning point coordinates can be extracted from the completed square form, with x-coordinate being the negative of the number inside the brackets.

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.