Question

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

Answer 1

Answer:

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

Step-by-step 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

$x_{v} = -\frac{b}{2a}$

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.