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)