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 ) (checked as correct)
identify the values of ( a ), ( b ), and ( c ).

Explanation:

Step1: Recall standard quadratic form

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

Step2: Analyze the given equation

The selected quadratic equation is \(0 = 4x^{2}+12x + 9\). By comparing with \(0 = ax^{2}+bx + c\):

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

Answer:

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