How does the discriminant of the equation defining the family relate to the equation of the envelope?

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 ... Recall from precalcu- lus algebra that if the discriminant b2 - 4ac is positive, the equation (2) has two distinct ... 2 ) + b(c1y0. 1 + c2y0. 2) + c(c1y1 + ... 17 In the quadratic formula, b2 − 4ac is called the discriminant. The function f(x) has a discriminant value of 8, and g(x) has a discriminant value of. Jul 14, 2023 ... When b2-4ac < 0 then there are no roots at all. Example: Find the discriminant of the equation x2+6x-5=0 1) Press [1] [sto ... 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 ... Hence, the nature of the roots α and β of equation ax2 + bx + c = 0 depends on the quantity or expression (b2 – 4ac) under the square root sign. We say this ... The quadratic formula, x=- b±sqrt(b^2-4ac)/2a, can be derived by completing the square on the general standard form a quadratic equation. 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. Feb 22, 2011 ... ... b2– 4ac < 0. We are now able to compute the coefficient of ... if n is sufficiently large, max (a, b) << c, c > 0 and b2– 4ac < 0 ... We know that b2 - 4ac is the discriminant (D). Thus, the vertex formula is: (h, k) = (-b/2a, -D/4a) where D = b2 ...