Question

which shows the correct substitution of the values a, b, and c from the equation 0 = 4x² + 2x − 1 into the quadratic formula below?
quadratic formula: $x = \frac{ -b \pm \sqrt{b^2 - 4ac} }{2a}$
\\(\circ\\) $x = \frac{ -2 \pm \sqrt{2^2 - 4(4)(-1)} }{2(4)}$
\\(\circ\\) $x = \frac{ -2 \pm \sqrt{2^2 - 4(4)(1)} }{2(4)}$
\\(\circ\\) $x = \frac{ -2 \pm \sqrt{2^2 + 4(4)(-1)} }{2(4)}$
\\(\circ\\) $x = \frac{ -2 \pm \sqrt{ -2^2 - 4(4)(-1) } }{2(4)}$

Explanation:

Step1: Identify a, b, c

For quadratic equation \(ax^2 + bx + c = 0\), given \(0 = 4x^2 + 2x - 1\) (or \(4x^2 + 2x - 1 = 0\)), we have \(a = 4\), \(b = 2\), \(c = -1\).

Step2: Substitute into quadratic formula

Quadratic formula is \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Substitute \(a = 4\), \(b = 2\), \(c = -1\):
\(x=\frac{-2\pm\sqrt{2^2 - 4(4)(-1)}}{2(4)}\)

Answer:

\(x = \frac{-2 \pm \sqrt{2^2 - 4(4)(-1)}}{2(4)}\) (the first option)