Answer:
![f(x)=5(x-2)^(2)+6](https://img.qammunity.org/2020/formulas/mathematics/middle-school/d94goqkuplw0e796hlhgx7t5is9y5duxt5.png)
Explanation:
we have
![f(x)=5x^(2) -20x+26](https://img.qammunity.org/2020/formulas/mathematics/middle-school/uegc31u3i2mq2z6m8w5rxu3josfipy7hfj.png)
This is the equation of a vertical parabola open upward
The vertex is a minimum
The equation of a vertical parabola in vertex form is equal to
![f(x)=a(x-h)^2+k](https://img.qammunity.org/2020/formulas/mathematics/high-school/7ipmrrobocsxyi038fh5rmhmhaf4i7cji9.png)
where
(h,k) is the vertex
Convert the given function to vertex form
Factor the leading coefficient
![f(x)=5(x^(2) -4x)+26](https://img.qammunity.org/2020/formulas/mathematics/middle-school/hgymae6xt3holhxhtje6h12vsfij3f7mgu.png)
Complete the square
![f(x)=5(x^(2) -4x+4)+26-20](https://img.qammunity.org/2020/formulas/mathematics/middle-school/g2zan4e68foglghufvxlyyydpzmfe3k9mu.png)
![f(x)=5(x^(2) -4x+4)+6](https://img.qammunity.org/2020/formulas/mathematics/middle-school/yhy19qg1x0hurdttw9y58o9e16jb6q88a4.png)
Rewrite as perfect squares
------> equation in vertex form
The vertex is the point (2,6)