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To rewrite the quadratic expression x^2 – 6x + 18 in the form of (x – a)^2 + b, where both a and b are integers, we will first complete the square. The process begins by focusing on the x^2 and -6x terms. We can take the coefficient of the x term, which is -6, divide it by 2 to obtain -3, and then square this result to get 9. This value will be used to facilitate the completion of the square.
Next, we can express the original quadratic by adding and subtracting this squared term within the expression. Thus, we rewrite x^2 – 6x + 18 as (x^2 – 6x + 9) + 9, which simplifies to (x – 3)^2 + 9. Here, we have successfully transformed the expression into the desired form, where a equals 3 and b equals 9, both of which are integers.
In conclusion, the expression x^2 – 6x + 18 can be represented as (x – 3)^2 + 9. This method of completing the square is a fundamental technique in algebra, particularly useful in various mathematical contexts, including preparation for examinations such as A Level Maths Easter Revision. Understanding this process not only aids in simplifying expressions but also enhances problem-solving skills in higher-level mathematics.
