# Thread: Writing equations for parabolas

1. ## Writing equations for parabolas

How do I do this?

Write an equation for the parabola whose vertex is (8, 6) and focus is (2, 6). Draw this parabola.

Thank you for reading my post.

2. Originally Posted by dazygrl02
How do I do this?

Write an equation for the parabola whose vertex is (8, 6) and focus is (2, 6). Draw this parabola.

Thank you for reading my post.
Hi dazygrl02,

If you sketch the graph...plot the vertex and focus...you will see that the parabola opens to the left.

The standard form for this parabola is $x=a(y-k)^2+h$, where $a<0$

Now, the vertex is at (h, k) which makes h = 8, and k = 6.

The focus is defined as $\left(h+\frac{1}{4a},{k}\right)$

Since your focus is at (2, 6), that would make $8+\frac{1}{4a}=2$

Solve for a.

Now you have a, h, and k.

Substitute into $x=a(y-k)^2+h$, and there you have it.