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 )

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

$$(2x)^2+2(2x)(3)+3^2=4x^2+12x+9$$

Step3: Rearrange to standard form

Set equation to $0$ by moving all terms to one side:
$$0=4x^2+12x+9$$

Answer:

D. $0 = 4x^2 + 12x + 9$