[EM_20151120QGXS] Quadratic Graphs by Completing the Square

Question

Introduction

     This “Elementary” Mathematics question is usually pitched at secondary 3 (» grade 9).  It is quite a standard type of question, but from my experience, many students do not know how to begin.  The wording of the question (especially part (a)) may throw off some people.  The first stage in solving any mathematics question is always to make sure you understand the question, to know what is expected of you.  Once this is done, this question is actually quite straightforward if you know what to do and know where to look.  The coefficient of  x²  is  a = 1, so the question is not that tricky.  Part (a) is simply instructing you to complete the square.

Review

 

Solution

Tip:  You could get the y-intercept by using your fingers to cover the x² and x terms.  There is an even faster way: just look at the constant term!  You get the answer  5  immediately!

Heuristics Used

H02. Use a diagram / model

H04. Look for pattern(s)

H05. Work backwards

H09. Restate the problem in another way

H11. Solve part of the problem

Suitable Levels

* GCE ‘O’ Level “Elementary” Mathematics

* any syllabus that includes quadratic functions and parabolas

* anyone who is interested