Question

given $y = (2x + 3)^2$, choose the standard form of the given quadratic equation.
\\(\circ\\) $0 = 25x^2$
\\(\circ\\) $0 = 4x^2 + 9$
\\(\circ\\) $0 = 4x^2 + 10x + 6$
\\(\circ\\) $0 = 4x^2 + 12x + 9$
complete
identify the values of $a$, $b$, and $c$.
$a = \square$
$b = \square$
$c = \square$
done

Explanation:

Step1: Recall Quadratic Standard Form

The standard form of a quadratic equation is \(ax^2 + bx + c = 0\), where \(a\), \(b\), and \(c\) are constants and \(a
eq0\).

Step2: Identify Coefficients from Given Equation

The given standard form of the quadratic equation (after expanding \(y=(2x + 3)^2\)) is \(0 = 4x^2+12x + 9\), which can be rewritten as \(4x^2+12x + 9 = 0\). Comparing this with \(ax^2+bx + c = 0\):

• For the \(x^2\) term, the coefficient \(a = 4\).
• For the \(x\) term, the coefficient \(b = 12\).
• For the constant term, \(c = 9\).

Answer:

\(a = 4\), \(b = 12\), \(c = 9\)