In parabola factoring and quadratic formula is not function there is any other formula your can?

Yes, there is another formula that can be used to find the roots of a quadratic equation, known as completing the square. This method involves manipulating the equation to create a perfect square trinomial, which can then be easily factored to find the roots.

Complete the Square

This method involves completing the square of the quadratic expression to factor it:

- Step 1: Move the constant term to the other side of the equation.
- Step 2: Divide both sides of the equation by the coefficient of x². This makes the coefficient of x² equal to 1.
- Step 3: Add and subtract the square of half the coefficient of x.
- Step 4: Factor the left-hand side as a perfect square trinomial.
- Step 5: Take the square root of both sides (remembering to include both the positive and negative roots).
- Step 6: Solve for x by isolating it on one side of the equation.

Example:

Factor the quadratic equation: x² + 6x + 8 = 0

Solution:

- Move the constant 8 to the other side: x² + 6x = -8
- Divide both sides by 1: x² + 6x = -8
- Add and subtract (6/2)² = 9: x² + 6x + 9 = 1
- Factor the left-hand side: (x + 3)² = 1
- Take the square root of both sides: x + 3 = ±1
- Solve for x: x = -3 ± 1

Therefore, the factors of the quadratic equation are (x + 2) and (x + 4).