Premium Only Content
 
			How to derive quadratic formula
Quadratic formula
The quadratic formula is a powerful tool for solving any quadratic equation. It is a formula used to find the roots (or solutions) of a quadratic equation in its standard form. A quadratic equation is a second-degree polynomial equation.
The Formula
The standard form of a quadratic equation is:
ax^2 + bx + c = 0
where a, b, and c are coefficients, with a not equal to 0.
The quadratic formula is:
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
To use it, you just need to identify the values of a, b, and c from your equation and plug them into the formula to solve for x. The "\pm" symbol means there are two possible solutions: one where you add the square root and one where you subtract it.
Key Components
* Discriminant: The expression under the square root, b^2 - 4ac, is called the discriminant. It tells you about the nature of the solutions without solving the entire equation.
* If b^2 - 4ac > 0, there are two distinct real solutions.
* If b^2 - 4ac = 0, there is exactly one real solution.
* If b^2 - 4ac < 0, there are two complex (non-real) solutions.
Common Applications
Quadratic equations and the quadratic formula are used in many real-world applications, especially in physics and engineering, to model situations that involve a parabolic path. Some examples include:
* Projectile Motion: Calculating the trajectory of a thrown ball, a launched rocket, or a bouncing object.
* Area and Geometry: Solving problems involving the area of a shape where the dimensions are related to a single variable.
* Business: Determining the maximum profit or minimum cost for a product.
* Engineering: Designing structures like suspension bridges and satellite dishes, which often use parabolic shapes.
- 	
				 2:57:52 2:57:52Laura Loomer6 hours agoEP154: Naturalized US Navy Medic From GAZA Exposed For Ties To Hamas23.2K15
- 	
				 35:45 35:45Stephen Gardner9 hours ago🔴BREAKING: Election Auditor EXPOSES Democrat Election Fraud Evidence!7.61K33
- 	
				 15:48 15:48Sponsored By Jesus Podcast13 hours agoHow to Stop Being JEALOUS | When Comparison Steals Your Joy243
- 	
				 LIVE LIVEDLDAfterDark4 hours agoDon't Worry - Things Will Get SO Much Worse! Sometimes It Be Like That222 watching
- 	
				 25:41 25:41Robbi On The Record9 hours agoThe Billion-Dollar Lie Behind OnlyFans “Empowerment” (Her Testimony Will Shock You) | part II1455
- 	
				 12:22 12:22Cash Jordan1 hour ago"CHICAGO MOB" Fights Back... "ZERO MERCY" Marines DEFY Judge, SMASH ILLEGALS2310
- 	
				 46:58 46:58Brad Owen Poker13 hours agoI Make QUAD ACES!!! BIGGEST Bounty Of My Life! Turning $0 Into $10,000+! Must See! Poker Vlog Ep 323321
- 	
				 2:52:28 2:52:28TimcastIRL4 hours agoSTATE OF EMERGENCY Declared Over Food Stamp CRISIS, Judge Says Trump MUST FUND SNAP | Timcast IRL190K113
- 	
				 3:22:45 3:22:45Tundra Tactical11 hours ago $14.20 earned🚨Gun News and Game Night🚨 ATF Form 1 Changes, BRN-180 Gen 3 Issues??, and Battlefield 6 Tonight!21.4K1
- 	
				 1:45:13 1:45:13Glenn Greenwald7 hours agoJD Vance Confronted at Turning Point about Israel and Massie; Stephen Miller’s Wife Screams “Racist” and Threatens Cenk Uygur with Deportation; Rio's Police Massacre: 120 Dead | SYSTEM UPDATE #54098.3K105