Write the equation of the parabola in vertex form.

Question

Vertex (0,4) (1,-1)

Answer 1

Hi Haley,

 

Here's the vertex form for a parabola that opens up or down:

 

     (y - k) = a(x - h)²

 

The vertex of the parabola is at (h, k), and a tells you something about how wide or narrow the parabola is.

 

For the parabola given above, you've got a vertex at (0, 4). So, h = 0 and k = 4:

 

     (y - 4) = a(x - 0)²

     (y - 4) = a(x)²

 

Now we just need to find a. The parabola passes through the point (1, -1), so let's plug in those values for x and y in order to solve for a:

 

     (-1 - 4) = a(1)²

     -5 = a

 

That should finish it! Now that we know h, k, and a, we can write out our final answer:

 

     (y - 4) = -5(x)²

 

Depending on your preferences, you can drop or keep the parentheses. Hope this has helped!