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 $0 = 4x^2 + 12x + 9$\
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: Simplify each term

Calculate the expanded terms.
$$(2x)^2+2(2x)(3)+3^2=4x^2+12x+9$$

Step3: Rearrange to standard form

Set $y=0$ to match the standard quadratic form $0=ax^2+bx+c$.
$$0=4x^2+12x+9$$

Step4: Identify a, b, c

Match coefficients to $ax^2+bx+c$.
$a=4$, $b=12$, $c=9$

Answer:

Standard form: $\boldsymbol{0=4x^2+12x+9}$
$a=4$, $b=12$, $c=9$