Question

What is the relevance of the vertex in physics and business applications?

Answer 1

So as we can see the vertex is useful in order to find maximum and minimum values. In physics is important because allow to calculate highest or minimum point on vertical motion for example. And on business is associated with minimum and maximum costs associated to a profit or revenue functions.

Explanation:

The vertex is a property when we have quadratic equations. The general equation for the quadratic polynomial is given by:

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

In order to find the vertx we can begin finding the x coordinate with the following formula:

`V_x = -(b)/(2a)`

And after have the x corrdinate we can find the y coordinate like this:

`P(V_x) = a(V_x)^2 + b(V_x) +c`

And the coordinate pair represent the vertex on this case:

`V = (V_x, V_y) = (-(b)/(2a),a(V_x)^2 + b(V_x) +c)`

If a>0 the parabola open upwards and on this case the vertex would represent a minimum

In the other case when a<0 the parabola open downwards and on this case the vertex would represent a maximum

So as we can see the vertex is useful in order to find maximum and minimum values. In physics is important because allow to calculate highest or minimum point on vertical motion for example. And on business is associated with minimum and maximum costs associated to a profit or revenue functions.