Question

kuta software - infinite algebra 2
using the quadratic formula
solve each equation with the quadr

1. ( v^2 + 2v - 8 = 0 )

Explanation:

Step1: Identify coefficients

For quadratic equation \(ax^2 + bx + c = 0\), here \(a = 1\), \(b = 2\), \(c = -8\).

Step2: Apply quadratic formula

Quadratic formula: \(v=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\)
Substitute values: \(v=\frac{-2\pm\sqrt{2^2 - 4(1)(-8)}}{2(1)}\)

Step3: Simplify discriminant

Calculate \(b^2 - 4ac\): \(4 + 32 = 36\)

Step4: Solve for v

\(v=\frac{-2\pm\sqrt{36}}{2}=\frac{-2\pm6}{2}\)
Two solutions:

• \(v=\frac{-2 + 6}{2}=\frac{4}{2}=2\)
• \(v=\frac{-2 - 6}{2}=\frac{-8}{2}=-4\)

Answer:

\(v = 2\) or \(v = -4\)