What is the vertex form of f(x)= 5x^2 +20x-16

Vertex of given quadratic function  is (-2,-36)

Step-by-step explanation:

Given function

We have to find the vertex of the given function .

The standard quadratic function is represented by  ,  

Where (h,k) represents the vertex and a ≠ 0.

If a is positive, the graph opens upward, and if a is negative, then it opens downward.

We first write the given equation in standard form ,by using completing square,

We know

First taking 5 common from function, we have,

Comparing we have, a = x and

-2ab= +4x ⇒ -2b = 4 ⇒ b = -2

Add and subtract b , we get,

On simplifying, we have,

We get,

On comapring with standard equtaion , we have h = -2 and k = -36

Thus, vertex of given quadratic function  is (-2 ,-36)

.

step-by-step explanation: