This study notes covers Worked Example 3: Finding Turning Point within Completing the Square for GCSE Mathematics. Revise Completing the Square in Algebra for GCSE Mathematics with 10 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 5 of 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example 3: Finding Turning Point
Find the turning point of y = x² + 4x − 3
Solution
Complete the square: (x + 2)² − 4 − 3 = (x + 2)² − 7
Turning point at x = −2, y = −7
Turning point: (−2, −7)
Practice questions for Completing the Square
To write x² + 10x + 3 in the form (x + p)² + q, what is the value of p?
Explain how you can tell from the completed square form whether a quadratic has a minimum or a maximum turning point.