# Writing the Equation of Parabolas

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

2. Substitute in h and k

3. Choose a coordinate to substitute in and solve for a.

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

2. Substitute in h and k

3. Choose a coordinate to substitute in and solve for a.

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

Remember the patterns:

**Examples:**

1. Find the equation of this parabola

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

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

Our vertex is (5, 3), 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, 5). We'll substitute 4 in for x and 5 for y.

Now we'll solve for a:

5 = a(1) + 3

2 = a

2 = a

To finish, we rewrite the pattern with h, k, and a:

2. Find the equation of the parabola:

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:

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

To finish, we rewrite the pattern with h, k, and a:

8 = 16a

1/2 = a

To finish, we rewrite the pattern with h, k, and a:

**Practice:**Find the equation of these parabolas.

**Answers:**1) 2) 3) 4) 5)

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