Write equations of parabolas in vertex form

The equation of a parabola in vertex form has one of the following 2 forms:

If the parabola is a vertical parabola, it will take the vertical form of the equation, and if the parabola is a horizontal parabola, it will take the horizontal form of the equation.

Here are the steps:

1. Determine which pattern to use (based on whether it is horizontal or vertical)

2. Substitute the values for h and k

3. Choose a coordinate along the parabola curve to substitute in and solve for parameter a.

4. Write your final equation with a, h, and k.

Here are 2 examples:

1. Find the equation of this parabola

Description: Description: Description: Description: Description: Description: Description: http://www.softschools.com/math/calculus/images/writing_the_equation_of_parabolas_img1.png

This is a vertical parabola, so we are using the pattern

Our vertex is (5, 3), so we will substitute those values in for h and k:

Now we must choose a point to substitute in. You can choose any point on the parabola except the vertex. Let's use (4, 5). We'll substitute 4 in for x and 5 for y.

Now we'll solve for a:

5 = a(1) + 3

2 = a

So now, we can rewrite the equation with h, k, and a:

2. Find the equation of the parabola:

Description: Description: Description: Description: Description: Description: Description: http://www.softschools.com/math/calculus/images/writing_the_equation_of_parabolas_img9.png

This is a vertical parabola, so we are using the pattern

Our vertex is (-4, -1), so we will substitute those numbers in for h and k:

Now we must choose a point to substitute in. You can choose any point on the parabola except the vertex. Let's use (4, 3). We'll substitute 4 in for x and 3 for y.

Now we'll solve for a:

4 = a(16) - 4

8 = 16a

1/2 = a

So now, we can rewrite the equation with h, k, and a: