The week in math we learned about at new way to solve quadratic equation using the quadratic formula which is a formula that uses the a quadratic equation in standard form and is important inorder to quickly determine wether a quadratic equation is solveable and can be in some situations a faster method in solving than the box method inspection or perfect square. I choose this topic because my physics teacher talked about using it in my kinematics units and it sounded interesting.

To use the quadratic equation , follow these steps:

1. Identify the coefficients: Determine the values of in the quadratic equation.

2. Plug into the quadratic formula: Substitute the coefficients into the quadratic formula:

This formula gives you the solutions (roots) for the quadratic equation.

3. Calculate the discriminant: Compute , which determines the nature of the roots:
– If , there are two distinct real roots.
– If , there is one real root.
– If , there are two non-real roots.

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Example:
Suppose we have the quadratic equation we dont have to change anyting since the coefficient for the high power is positive and all the terms are on one side .

1. Identify .
2. Plug into the quadratic formula:

Simplify to get:



So, the solutions are and .

3. Calculate the discriminant:

Since the discriminant is positive, there are two distinct real roots.

Therefore, the solutions to the quadratic equation are and .