Can the discriminant be used to find the length of the latus rectum of a parabola?

... b2​=a(x+2ab​)2 ... −(b2 − 4ac) = 4ac − b2. The formula for h has a denominator of 2a; double ... The discriminant of a quadratic is the expression inside the radical of the quadratic formula. b2−4(ac) b 2 - 4 ( a ... Jan 5, 2022 ... (-12+√(b^2-4ac))/2a. (where a = 1, b = 5, c = 3). How do I write a ... Δ = b^2 - 4ac; x = (-b ± √Δ)/2a. And the most important one, in ... ... byĵ + bzk̂ Magnitudes: |a⃗|=√{ax2 +ay2+az2} |b⃗|=√{bx2 +by2+bz2} Scalar ... 4ac}}/{2a} Work (W), Mechanical Energy (E, Kinetic Energy (K)) ... However, we know there must be another independent solution. It's not obvious what that might be, but let's make the educated guess y(t) = C2teλ1t. The discriminant is 0, so the root is rational and the equation can be solved by factoring. In. , substitute: Since. , the equation has 2 real roots. b2 4ac>0. ... 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. Jun 20, 2014 ... ... (b2-4ac ≥ 0) ⇒ (x = {-b-√{b2-4ac}}/{2a}) \lor (x = {-b+√{b2-4ac}}/{2a}). Please write complete proofs in each subquestion, without ... ... 2 (x + (b / 2a))2 = -4ac / 4a2 + b2 / 4a2 x + (b / 2a)2 = (b2 - 4ac) / 4a2 x + (b / 2a) = +/- sqrt ((b2 - 4ac) / 4a2) x = -b / 2a +/- sqrt(b2 - 4ac) / 2a Because the value of b2 – 4ac is less than zero, this equation will not have real solutions. Our answer will be 2x2 – 4x + 5 = 0. If we inspect all of the other ...