Question

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

Explanation:

Step1: Expand the squared binomial

Use the formula $(a+b)^2=a^2+2ab+b^2$, where $a=2x$, $b=3$.
$$(2x+3)^2=(2x)^2+2(2x)(3)+3^2$$

Step2: Calculate each term

Compute the value of each expanded term.
$$(2x)^2+2(2x)(3)+3^2=4x^2+12x+9$$

Step3: Rearrange to standard form

Set the equation to $0$ by subtracting $y$ from both sides, substitute $y=4x^2+12x+9$.
$$0=4x^2+12x+9$$

Answer:

0 = 4x² + 12x + 9