Why is '-4ac' subtracted from b² in the discriminant?

Jun 12, 2017 ... The question asks whether entire parabola is below x-axis. This will happen if discriminant is negative AND the parabola opens downward. We know that b2 - 4ac is the discriminant (D). Thus, the vertex formula is: (h, k) = (-b/2a, -D/4a) where D = b2 ... term with B + D. The result is. T. C2 — A2. B2. — D2. 1. V 2 H ~ 2 A H [ A C ( A + C)2. +. BD(B+D)2\. <2>. Now a quantity like (.A + C)2 = 4AC + (A - C)2 may be ... Solve for a variable, factor, expand, evaluate fractions, linear equations, quadratic equations, inequalities, systems of equations, matrices. Then, the discriminant A = b2-4ac satisfies: △ < a². Proof. If the ... + b 2 − a) . In conclusion, we believe that Lemma 1 can be a nice starting. Oct 2, 2022 ... Find all the roots of the solution, and compute the distance between successive roots to see that it is a constant. What is the probability that the equation Ax2 + Bx + C = 0 has two real roots? This is P(B2 - 4AC > 0). Note that since A,B,C ∈ [0, 1], if we ... Which of the following statements are true of the discriminant? ... The discriminant is b 2 - 4ac in the quadratic formula. The discriminant is the radicand of ... ... 2 + q, the graph of y = f(x) has a turning point at (−p, q). • For the quadratic equation ax2 + bx + c = 0, the expression b2 – 4ac is called the discriminant. (b) The point P = (1,−1,2) lies on both the paraboloid x2+y2 = z and the ... If a 6= 0 and b2 − 4ac > 0, then y has the form c1eαx + c2eβx where α ...