Glossary Checklist FAQ

E. Completing the Square

The standard form of quadratic functions is useful for determining \(x\)- and \(y\)-intercepts, and for discussing the direction the graph opens (the value of \(a\)). What would be even more helpful would be the ability to investigate quadratic functions in both vertex and standard form. When given the vertex form, you can easily expand the function and simplify to express the equation of the function in standard form. There is also a way to convert from standard form, into vertex form, called completing the square. It is a slightly more difficult process, so practice is required!


 Investigation

Perfect Square Trinomials


  1. Complete the following table comparing perfect square trinomials; trinomials that are a result of squaring a binomial.

    Exponent Form
    		Binomial Form
    		 Perfect Square Trinomial
    \((x + 5)^2\)  \((x + 5)(x + 5)\)
    		 \(x^2 + 10x + 25\)
     \((x - 10)^2\)    
     \((x - 8)^2\)    
     \((x + 3)^2\)    


  2. What do you notice when you compare the binomial and the coefficient of the second term in the trinomial?


  3. What do you notice when you compare the binomial and the constant term (last term) in the trinomial?