How to solve a general quadratic equation for x to find the quadratic formula.

Solution Preview

The quadratic formula (x = (-b ± √(b²- 4ac))/2a) is the easiest way to solve an equation of the form ax² + bx + c = 0. But why is the formula true?

We start with a general quadratic equation: y = ax² + bx + c. Here, x and y are unknown variables, and a, b, and c stand for any number (we use the letters instead of specific numbers to show that the quadratic formula will work no matter what numbers we plug in to a, b, and c).

We want to know what values for x will make y equal to zero. ...

Solution Summary

This solution has a proof of the quadratic formula.

... Solve by using the quadratic formula: 2x2 + 5x - 3 = 0. ... Graph the quadratic equation and state the domain and ... each problem as to how the answers were derived. ...

... b. We use the same equation and derivation of units earlier, except that s now is ... Using the quadratic formula, we can solve for the values of t: (4)2 − 4(1 ...

... in the Euler-Maclaurin formula (10) decays exponentially, the ... a constant term and a quadratic term and ... that does exist but the mathematical derivation that led ...

... contains : 1. Average and marginal revenue curves formulas, schedules 2 ... (a) Derive the total ... and relationship between quantity and total revenue is quadratic. ...

... through the integration (or better yet, derived through a ... we use n = 2 (a quadratic interpolating polynomial ... can be computed to attain the formula for Simpson's ...

... 4. Derive the quadratic and linear equations from the corresponding graphs of a classmate. W eek 6/2. ... (ii) Quadratic formula. (iii) Completing the square. ...

... 4. Derive the quadratic and linear equations from the corresponding graphs of a ... 1. Solving by factorization 2. by quadratic formula 3. Completing the square ...

... Before we continue, we derive a formula for an =r an−1+ d ... homogeneous and quadratic not linear ... If we continue, this suggests the formula nn an =( 3n ) ( 3 ( n ...

... now need to solve (11) using the general formula to solve ... case A = 1, B = 2.521, C = 0.607 in quadratic (11 ... We now use identity (4) derived earlier to find out ...