Derive the quadratic formula from the standard form (ax2 + bx + c = 0) of a quadratic equation by following the steps below.
1. divide all terms in the equation by a.
2. subtract the constant (the term without an x) from both sides.
3. add a constant (in terms of a and b) that will complete the square.
4. take the square root of both sides of the equation.
5. solve for x.

The result is the well-known quadratic formula: x = (-b±√(b²-4ac))/(2a)

Step-by-step explanation:

Start with the standard form quadratic equation:

ax² +bx +c = 0

1. Divide by a

x² +(b/a)x +(c/a) = 0

2. Subtract the constant

x² +(b/a)x = -(c/a)

3. Complete the square

x² +(b/a)x + (b/(2a))² = (b/(2a))²-(c/a)

(x +b/(2a))² = (b²-4ac)/(2a)²

4. Take the square root

x +b/(2a) = ±√(b²-4ac)/(2a)

5. Subtract the constant on the left to get x by itself

x = (-b±√(b²-4ac))/(2a)

b.an increase in a causes b to decrease