What is the maximum of

Question

8x-x^2?

Answer 1

Finding minimum and maximum values :

To find the maximum or minimum value of a quadratic function, by completing the square of the quadratic function.

Rewrite the function in standard form,

i.e, .

So, the vertex of the graph of f  is , which implies the following.

Minimum and maximum values of quadratic functions

Consider the function with vertex .

1. If , f  has a minimum at .The minimum value is .

2. If , f  has a maximum at .The maximum value is .

The function is y = 8x - x ².

Compare the above function with .

a = - 1, b = 8, and c = 0.

Rewrite the function in standard form : .

So, the vertex of the graph of f is

Vertex = .

a < 0, so, f  has a maximum at .

The maximum value is  .

Therefore, the maximum value is 16.

Answer 2

The maximum value is  .

Therefore, the maximum value is 16.