How to Factor a Parabola

Upward parabola

To figure out the vertex of a parabola, you will need to factor out the equation given. The result will be two points where the vertex will have on the graph. When taking a geometry or algebra class, you will need to know how to work with parabolas and will need to know how to factor. Here are some basic steps to follow.

Instructions

1. Follow the formula. The function will appear f(x) = a(x-h)^2 + k. Take away number without an X next to it on each side of expression. For example, y = x^2 + 2x - 25. Subtract each side of the equation by -25. Therefore, you will have 0 = x^2 + 2x.

2. Determine what needs to be factored first. Using the example of f(x) = 2(x^2-4x) +7 you result with 2x^2 - 8x + 7. Then factor out the 2. After factoring out the 2 you will end up 2(x^2 - 4x + 4) + 7. Find two places where the X is equal to zero. You will need to factor what is left in the expression. This will appear as 0 = x (x +2) which will make x = 0 or -2.

3. Complete the square of the equation. From 2(x^2 - 4x + 4) + 7 will result (x^2 -4x) + 7 - 8.

4. Factor again and simplify. From (x^2 - 4x) +7 - 8, you will end up with 2 (x-2) -1.

5. Find the answer to the equation. The points to the vertex would be (2,-1) since 2 = x and -1 is the minimum value. Finally, since 2(x-2) -1 is more than or equal to 0, it shows that the parabola will open upward on the graph.