Question

convert the quadratic function below to standard form:
$(x + 5)^2 - 6$
standard form: $square x^2 + square x + square$

Explanation:

Step1: Expand \((x + 5)^2\)

Using the formula \((a + b)^2 = a^2 + 2ab + b^2\), where \(a = x\) and \(b = 5\), we get \((x + 5)^2 = x^2 + 2\times x\times5 + 5^2 = x^2 + 10x + 25\).

Step2: Subtract 6 from the expanded form

Now we have \((x + 5)^2 - 6 = (x^2 + 10x + 25) - 6\). Simplifying the constant terms, \(25 - 6 = 19\), so the expression becomes \(x^2 + 10x + 19\).

Answer:

1 \(x^2\) + 10 \(x\) + 19