Tempestt is a mathematics student who has been tasked with creating a graph to represent a function with a maximum located at (-4,2). In order to complete this task, Tempestt will need to understand the basics of graphing functions and how to identify the location of the maximum of a graph.
Tempestt’s Graph
Tempestt begins by plotting the graph of the given function, which is a parabola. This parabola opens downward, meaning that the maximum of the graph is located at its vertex. By using her knowledge of the properties of parabolas, Tempestt is able to identify that the vertex of the graph is located at (-4,2).
Tempestt then labels the vertex of the graph with a point, which is the maximum of the graph. She also labels the x-axis and y-axis of the graph with the corresponding numbers, so that the maximum point can be easily identified.
Maximum at (-4,2)
Once the maximum point has been identified, Tempestt can then determine the equation of the graph. By using her knowledge of equations of parabolas, Tempestt is able to determine that the equation of the graph is y = x^2 – 8x + 14. This equation can then be used to determine the exact coordinates of the maximum point, which is (-4,2).
Tempestt then adds a line of best fit to the graph, which helps to illustrate the shape of the parabola more clearly. This line of best fit is also useful for determining the exact coordinates of the maximum point.
In conclusion, Tempestt has successfully created a graph to represent a function with a maximum located at (-4,2). By using her knowledge of the properties of parabolas and equations of parabolas, Tempestt is able to identify the maximum point of the graph and label it accordingly. She then adds a line of best fit to the graph in order to illustrate the shape of the parabola more clearly.
Tempestt has found a way to graph a function that has a maximum located at the point (–4, 2). Her graph looks like the following:
The graph shows a parabola opening downward with its vertex at the point (–4, 2). The maximum point is represented as the highest order point with the highest y-coordinate (2). By looking at the graph, it is clear that the function is decreasing for all values of x less than –4 and increasing for all values of x greater than –4. Also, the graph shows that the function reaches its maximum value of 2 only at the point (–4, 2).
Given the information, the graph is a correct representation of a function that has a maximum located at (–4, 2); hence, this could be Tempestt’s graph. Furthermore, a fact that can be deduced from the graph is that the function never takes on a negative value, since the x-coordinate is always less than or equal to zero.
In conclusion, Tempestt has accurately graphed a function that has a maximum located at (–4, 2) by plotting a parabola with its vertex at the point (–4, 2). As a result, this could indeed be her graph.
