Question

What is the vertex of the graph f(z)= 2z² +82 +37

Answer 1

The vertex of the function is located at coordinates (119, 0).

Explanation:

1. Write the function and simplify it.

`f(z)= 2z^(2)+82+37\\ \\f(z)= 2z^(2)+119`

2. Find the derivative with respect to z.

Check the attached image.

`(d)/(dz) (2z^(2)+119)\\ \\f'(z)=2*2z^(2-1)\\ \\f'(z)=4z`

3. Find the roots of the resulting function.

`f'(z)=4z\\ \\4z=0\\ \\z=0`

4. Evaluate the calculated value in the original function.

`f(0)= 2(0)^(2)+119\\ \\f(0)=119`

5. Conclude.

The vertex of the function is located at coordinates (0, 119).