Question

which equation has an ( a )-value of 1, a ( b )-value of ( -3 ), and a ( c )-value of ( -5 )?
( 0 = 3x - 5 - x^2 )
( 0 = -3x - 5 + x^2 )
( 0 = -3x + 5 - x^2 )
( 0 = x - 3 - 5x^2 )

Explanation:

Step1: Recall quadratic form

The standard quadratic equation is \(0 = ax^2 + bx + c\), where \(a\), \(b\), \(c\) are coefficients.

Step2: Analyze each option

• First option: \(0 = 3x - 5 - x^2\) can be rewritten as \(0=-x^2 + 3x - 5\). Here, \(a=- 1\), \(b = 3\), \(c=-5\) (not matching).
• Second option: \(0=-3x - 5 + x^2\) can be rewritten as \(0=x^2-3x - 5\). Here, \(a = 1\), \(b=-3\), \(c=-5\) (matches the given values).
• Third option: \(0=-3x + 5 - x^2\) can be rewritten as \(0=-x^2-3x + 5\). Here, \(a=-1\), \(b=-3\), \(c = 5\) (not matching).
• Fourth option: \(0=x - 3 - 5x^2\) can be rewritten as \(0=-5x^2+x - 3\). Here, \(a=-5\), \(b = 1\), \(c=-3\) (not matching).

Answer:

\(0 = -3x - 5 + x^2\) (the second option)