Answer : d. minimum (-1,3)
![f(x) = 5x^2 + 10x + 8](https://tex.z-dn.net/?f=f%28x%29%20%3D%205x%5E2%20%2B%2010x%20%2B%208)
The vertex form of quadratic function is
, where (h,k) is the vertex
To get vertex form we apply completing the square method
To apply completing the square method , there should be only x^2
So we factor out 5 from from first two terms
![f(x) = 5(x^2 + 2x) + 8](https://tex.z-dn.net/?f=f%28x%29%20%3D%205%28x%5E2%20%2B%202x%29%20%2B%208)
Now we take the number before x (coefficient of x) and divide by 2
=1
Now square it
![(1)^2 =1](https://tex.z-dn.net/?f=%281%29%5E2%20%3D1)
Add and subtract 1 inside the parenthesis
![f(x) = 5(x^2 + 2x + 1 - 1) + 8](https://tex.z-dn.net/?f=f%28x%29%20%3D%205%28x%5E2%20%2B%202x%20%2B%201%20-%201%29%20%2B%208)
Now we take out -1 by multiplying 5
![f(x) = 5(x^2 + 2x + 1) -5 + 8](https://tex.z-dn.net/?f=f%28x%29%20%3D%205%28x%5E2%20%2B%202x%20%2B%201%29%20-5%20%2B%208)
![f(x) = 5(x^2 + 2x + 1) + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D%205%28x%5E2%20%2B%202x%20%2B%201%29%20%2B%203)
Now we factor x^2 +2x+1 as (x+1)(x+1)
![f(x) = 5(x+1)(x+1) + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D%205%28x%2B1%29%28x%2B1%29%20%2B%203)
![f(x) = 5(x+1)^2 + 3](https://tex.z-dn.net/?f=f%28x%29%20%3D%205%28x%2B1%29%5E2%20%2B%203)
h=-1 and k=3
So vertex is (-1,3)
When the value of 'a' is negative , then it is a maximum
When the value of 'a' is positive , then it is a minimum
is in the form of ![f(x) = ax^2 + bx + c](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c)
The value of a is 5
5 is positive so it is a minimum
f(x) is minimum at point (-1,3)