How to Find the Roots of a Parabola by Factoring

To find the roots of a parabola using factoring, follow these steps:

1. Write the quadratic equation in standard form: A quadratic equation has the form ax² + bx + c = 0. Make sure your equation is arranged properly.
2. Factor the quadratic: Look for two numbers that multiply to give you ac (the product of a and c) and add up to b. For example, if your quadratic is x² + 5x + 6 = 0, you need two numbers that multiply to 6 and add to 5. These numbers are 2 and 3.
3. Rewrite the equation: Use the numbers from the previous step to rewrite the equation in factored form. For our example, this becomes (x + 2)(x + 3) = 0.
4. Set each factor to zero: Solve for x in each of the equations you formed from the factors: x + 2 = 0 and x + 3 = 0. Thus, you get x = -2 and x = -3.
5. Write the roots: The solutions x = -2 and x = -3 are the roots of the parabola.

By following these steps, you can easily find the roots of a parabola by factoring. This method works well when the quadratic can be factored into simple binomials.