Answer:
![y=(x-3)^{2} -25](https://tex.z-dn.net/?f=y%3D%28x-3%29%5E%7B2%7D%20-25)
Step-by-step explanation:
The standard form of a quadratic equation is ![y=ax^{2} +bx+c](https://tex.z-dn.net/?f=y%3Dax%5E%7B2%7D%20%2Bbx%2Bc)
The vertex form of a quadratic equation is ![y=a(x-h)^{2} +k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E%7B2%7D%20%2Bk)
The vertex of a quadratic is (h,k) which is the maximum or minimum of a quadratic equation. To find the vertex of a quadratic, you can either graph the function and find the vertex, or you can find it algebraically.
To find the h-value of the vertex, you use the following equation:
![h=\frac{-b}{2a}](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-b%7D%7B2a%7D)
In this case, our quadratic equation is
. Our a-value is 1, our b-value is -6, and our c-value is -16. We will only be using the a and b values. To find the h-value, we will plug in these values into the equation shown below.
⇒ ![h=\frac{-(-6)}{2(1)}=\frac{6}{2} =3](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-%28-6%29%7D%7B2%281%29%7D%3D%5Cfrac%7B6%7D%7B2%7D%20%3D3)
Now, that we found our h-value, we need to find our k-value. To find the k-value, you plug in the h-value we found into the given quadratic equation which in this case is ![y=x^{2} -6x-16](https://tex.z-dn.net/?f=y%3Dx%5E%7B2%7D%20-6x-16)
⇒
⇒
⇒ ![y=-25](https://tex.z-dn.net/?f=y%3D-25)
This y-value that we just found is our k-value.
Next, we are going to set up our equation in vertex form. As a reminder, vertex form is: ![y=a(x-h)^{2} +k](https://tex.z-dn.net/?f=y%3Da%28x-h%29%5E%7B2%7D%20%2Bk)
a: 1
h: 3
k: -25
![y=(x-3)^{2} -25](https://tex.z-dn.net/?f=y%3D%28x-3%29%5E%7B2%7D%20-25)
Hope this helps!