Question

What is the vertex of the function `f( x ) = - 5x ^ { 2} + x + 3`?

Answer 1

Vertex is at `(0.1,3.05)`

Explanation:

`f(x)= -5x^2+x+3 = -5(x^2-0.2x)+3` or

`f(x)= -5(x^2-0.2x +0.1^2)+0.5+3` or

`f(x)= -5(x- 0.1)^2+3.05`. This is vertex form of equation.

Comparing with standard vertex form of equation

`f(x)=a(x-h)^2+k ; (h,k)` being vertex we find here

`h= 0.1 , k=3.05 :.` Vertex is at `(0.1,3.05)` [Ans]