Question

given $y = (2x + 3)^2$, choose the standard form of the given quadratic equation.
○ $0 = 25x^2$
○ $0 = 4x^2 + 9$
○ $0 = 4x^2 + 10x + 6$
○ $0 = 4x^2 + 12x + 9$
done

Explanation:

Step1: Expand the square

Using the formula \((a + b)^2 = a^2 + 2ab + b^2\), where \(a = 2x\) and \(b = 3\). So \((2x + 3)^2=(2x)^2+2\times(2x)\times3 + 3^2\)

Step2: Simplify each term

\((2x)^2 = 4x^2\), \(2\times(2x)\times3 = 12x\), \(3^2 = 9\). Then \(y=(2x + 3)^2=4x^2+12x + 9\)

Step3: Rewrite in standard form

The standard form of a quadratic equation is \(ax^2+bx + c = 0\) (or \(0=ax^2+bx + c\)). So we rewrite \(y = 4x^2+12x + 9\) as \(0=4x^2+12x + 9\) (by subtracting \(y\) from both sides, but since we just need the standard form of the quadratic expression from \(y=(2x + 3)^2\) to \(0 = ax^2+bx + c\), we can directly expand and rearrange).

Answer:

\(0 = 4x^2 + 12x + 9\) (the last option: \(0 = 4x^2 + 12x + 9\))