What is the first step to complete the square when a > 1?

Disable ads (and more) with a premium pass for a one time $4.99 payment

Prepare for the GCSE Maths Exam with our interactive quizzes. Study with a variety of questions and detailed explanations. Enhance your skills and boost your confidence before the exam day!

To complete the square for a quadratic expression of the form ( ax^2 + bx + c ) where ( a > 1 ), the first step is to factor out the coefficient ( a ) from the terms that involve ( x ). This is crucial because it allows us to work with a simpler quadratic expression in the standard form, making it easier to manipulate.

When you factor out ( a ), you rewrite the expression as ( a(x^2 + \frac{b}{a}x) + c ). This is essential because completing the square involves adjusting the ( x ) terms into a perfect square trinomial. By isolating the quadratic portion, you set up for the next steps, such as finding the term needed to complete the square for ( x^2 + \frac{b}{a}x ).

From here, one could determine the necessary constant to complete the square successfully. However, without factoring out ( a ) first, the subsequent steps become more complex, hindering the ability to properly transform the quadratic expression into vertex form. Thus, starting with the factorization is the appropriate initial step in this process.

Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy