Question

(a) determine, without graphing, whether the function has a minimum value or a maximum value f(x) = 2x -8x -5

Answer 1

The leading coefficient is positive, which means that the function has a minimum value.

Explanation:

Vertex of a quadratic function:

Suppose we have a quadratic function in the following format:

`f(x) = ax^(2) + bx + c`

It's vertex is the point
`(x_(v), f(x_(v))`

In which

`x_(v) = -(b)/(2a)`

If a<0, the vertex is a maximum point, otherwise, it is a minimum point.

In this question:

`f(x) = 2x^2 - 8x - 5`

So
`a = 2 > 0`, which means that the function has a minimum value.