The quadratic formula is a technique that can be used to solve quadratics, but in order to solve the problem, it must be in the correct form. The quadratic must be in the form of the quadratic equation: ax2 + bx + c = 0. In other words, the quadratic must be in descending order (highest power to lowest power) and equal to zero making it easy to identify the values of a, b, and c to plug into the quadratic formula.
The quadratic formula is generally used to solve all quadratics in the form ax2 + bx + c = 0 and will find the solution to the problem every time. However, there are times when other solving techniques are faster and should be considered.
Consider the following problems:x 2 – 6x – 17 = 0 → This problem can be solved using the quadratic formula, but it would be faster to solve the problem by factoring. Generally, factoring should be considered if the leading coefficient is a 1, meaning the problem is in the form x2 + bx + c = 0.
2(x – 4)2 – 6 = 0 → This problem could be solved using the quadratic formula, but we would need to simplify the problem first in order to get the problem in the correct form. A better option would be to use the square root principle.
Here is the quadratic formula:
The quadratic formula is used frequently throughout mathematics. When solving a problem using the quadratic formula here are the steps we should follow for each problem:
Step 1: Simplify the problem to get the problem in the form ax2 + bx + c = 0.
Step 2: Identify the values of a, b, and c, then plug them into the quadratic formula.
Step 3: Simplify the numbers within the quadratic formula.
Step 4: Simplify the radical and reduce/simplify to get the final answer.