Tempestt Graphs A Function That Has A Maximum Located At (–4, 2). Which Could Be Her Graph?

Tempestt Graphs A Function That Has A Maximum Located At (–4, 2). Which Could Be Her Graph?

f(x) = -(x+4)^2 + 2

The function has a negative sign in front of the squared term which shows that this is a downward opening parabola. And the vertex at (-4, 2) is the point of maximum.

We can rewrite this function in vertex form to see why this is the case

f(x) = a(x-h)^2 + k

Where an is the coefficient before the squared term and (h, k) is the vertex of the parabola. Examining this structure to the original function indicates that:

a = -1

h = -4

k = 2

Now, after we plug these values into the vertex form, we get the value:

f(x) = -(x+4)^2 + 2

This value confirms that the function has a maximum at (-4, 2).

To ensure that this is a genuine graph for Tempestt’s function, we can examine the function’s behaviour as x approaches infinity and negative infinity. Because the parabola is downward-opening, the function will approach negative infinity as x reaches positive or negative infinity. This suggests that the graph will have a “U” form, with the vertex located at the maximal point.

Another possible function that Tempestt have graphed, which also has a maximum at (-4, 2), is called the cubic function:

f(x) = -(x+4)^3 + 2

As you can see, this function is also a downward-opening curve, peaking at (-4, 2). The curve has a more noticeable and sharp shape than a quadratic function. Moreover, it reaches negative infinity faster as x approaches positive or negative infinity.

To summarise, Tempestt function may have graphed a quadratic or cubic function with a maximum at (-4, 2). By studying the graph’s structure and the function’s behaviour as x approaches infinity and negative infinity, we may find that either of these functions could be a suitable description of Tempestt’s graph.

However, it is worth noticing that many additional functions might have a maximum at (-4, 2). Their forms would differ from the quadratic or cubic functions outlined above. For example, a quartic function with a maximum at (-4, 2) has two more turning points, and the graph would be more complex than a quadratic or cubic function. Similarly, a trigonometric function with a maximum at (-4, 2) would be periodic, with maximums occurring at regular intervals.

Besides, a function with a maximum at (-4, 2) meets certain requirements. For example, the function must be continuous at (-4, 2), with a negative second showing that it is concave downward. These requirements ensure that the function has a local maximum at (-4, 2) and that the graph has the proper shape at that point.

It is an important topic in calculus since it enables us to comprehend the position and behaviour of maxima and minima when dealing with functions in different contexts. For instance in economics we look for the level of output that will maximise the profit given a product while in physics we need to find the path which takes the shortest time to travel from one site to another.

Final Words

Different types of functions could have a maximum located at (-4, 2), but a quadratic or cubic function are two examples that have a simple shape. By understanding the conditions which satisfy a function to have a maximum or minimum at a particular point, we can study and optimise functions in a wide range of applications.