Question

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

Explanation:

Step1: Expand the square term

We start with the given quadratic function \((x + 5)^2-6\). First, we expand \((x + 5)^2\) using the formula \((a + b)^2=a^2+2ab + b^2\), where \(a = x\) and \(b = 5\). So, \((x + 5)^2=x^2+2\times x\times5 + 5^2=x^2 + 10x+25\).

Step2: Simplify the expression

Now we substitute the expanded form back into the original function: \((x^2 + 10x+25)-6\). Then we simplify by combining the constant terms: \(x^2+10x+(25 - 6)=x^2+10x + 19\).

Answer:

The standard form of the quadratic function \((x + 5)^2-6\) is \(x^2+10x + 19\), so the blanks should be filled with \(1\) (coefficient of \(x^2\)), \(10\) (coefficient of \(x\)), and \(19\) (constant term) respectively. In the standard form \(ax^2+bx + c\), we have \(a = 1\), \(b = 10\), \(c = 19\). So the standard form is \(x^2+10x + 19\).