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 ) identify the values of ( a ), ( b ), and ( c ) ( a = ) ( b = ) ( c = )

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 $y=0$ for standard quadratic form $0=ax^2+bx+c$:
$$0=4x^2+12x+9$$

Step4: Match coefficients to $ax^2+bx+c$

Identify $a$, $b$, $c$ from the standard form.

Answer:

$a=4$, $b=12$, $c=9$