what is the formula for quadratic???

⚑ Flag

The quadratic formula is derived from solving the parent equation of quadratic graphs, f(x) = ax^2 + bx + c.(For the sake of example, f(x) = 0)(The original quadratic equation)ax^2 + bx + c = 0(Subtract c from both sides)ax^2 + bx = -c(Divide both sides by a)x^2 + (bx)/a = -c/a(Complete the square in the next step)x^2 + (bx)/a + b^2/(4a^2) = -c/a + b^2/(4a^2)(Square root both sides since left is now a perfect square trinomial)x + (bx)/a = ±√( -c/a + b^2/(4a^2) )(Subtract -(bx)/a from both sides)x = -(bx)/a ± √( -c/a + b^2(4a^2) )(Multiply -c/a by 4a/4a to get common denominators)x = -(bx)/a ± √( -(4ac)/(4a^2) + b^2(4a^2) )(Simplify the terms inside the radical)x = -b ± √( b^2 - 4(a)(c) ) / (2a)So, the quadratic formula is:x = -b ± √( b^2 - 4(a)(c) ) / (2a)