Solving Equations using the Quadratic Formula

We can use the Quadratic Formula to solve equations of the form ax² + bx + c = 0

Where a, b, and c are real numbers .

Quadratic Formula to “Pop goes the Weasel”
x equals Positive -for.html">negative b
plus or minus the square root
of b squared minus four a c
ALL over two a .

The discriminant b² – 4ac is part of the quadratic formula

Steps to Solve using the Quadratic Formula
1. Write in Standard Form. Set ax² + bx + c = 0
2. Find the discriminant. (b² – 4ac)
3. Substitute a , b, and c into the Quadratic Formula
4. Simplify if possible .
5. Find the approximate values on Calculator .

Example:

2x2 + 6x = 3 ------------------->	2x2 + 6x = 3
1. Write in standard form set equal to zero .	2x2 + 6x – 3 = 3 – 3 2x2 + 6x – 3 = 0
2. Find the discriminant b2 – 4ac	a = 2  b = 6   c = -3 b2 – 4ac = (6)2 – 4(2)(-3) = 60 Two irrational solutions.
3. Substitute a, b, and c into the Qudratic Formula 4. Simplify.

Answers: Exact values

Approximate values
x = 0.44 and x = -3.44