Whats the quadratic formula??

a x ^ 2 + b x + c = 0

the quadratic formula shows which values of x solve the general quadratic equation shown above:

x = [-b ± √(b2-4ac)]/2a

just do a web search on it and you will find many explanations on how it is derived and used.

The quadratic formula is a mathematical equation used to find the solutions (or roots) of a quadratic equation in the form of ax^2 + bx + c = 0, where 'a', 'b', and 'c' are constants.

The quadratic formula states that for any quadratic equation in the form mentioned above, the solutions for 'x' can be found using the following formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

To explain how to get the quadratic formula, the first step is to understand the process of solving a quadratic equation. There are different methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula.

The quadratic formula itself can be derived through the process of completing the square. Starting with the quadratic equation in standard form, ax^2 + bx + c = 0, you can follow these steps to derive the quadratic formula:

1. Divide the entire equation by 'a' to make the coefficient of the x^2 term equal to 1: x^2 + (b/a)x + c/a = 0

2. Move the constant term (c/a) to the right side of the equation: x^2 + (b/a)x = - c/a

3. To complete the square, take half of the coefficient of 'x', square it, and add it to both sides of the equation. In this case, take (b/2a), square it [(b/2a)^2 = b^2/4a^2], and add it to both sides: x^2 + (b/a)x + (b^2/4a^2) = - c/a + (b^2/4a^2)

4. Simplify the right side of the equation: x^2 + (b/a)x + (b^2/4a^2) = (b^2 - 4ac)/4a^2

5. Write the left side of the equation as a perfect square trinomial: (x + b/2a)^2 = (b^2 - 4ac)/4a^2

6. Take the square root of both sides to solve for x + b/2a: √((x + b/2a)^2) = ± √((b^2 - 4ac)/4a^2)

7. Simplify the left side: x + b/2a = ± √(b^2 - 4ac)/2a

8. Finally, isolate 'x' by subtracting b/2a from both sides: x = (-b ± √(b^2 - 4ac))/2a

This is the quadratic formula that can be used to find the solutions of any quadratic equation.