Considering the vertex of the graph, it is found that the quadratic function that is the best model for the data is given by:
The equation of a quadratic function, of vertex (h,k), is given by:
In which a is the leading coefficient.
Researching the problem on the internet, it is found that the vertex is at point (4,800), hence h = 4 and k = 800.
It has a value of y = 0 at x = 6, hence:
Thus, the model is:
More can be learned about quadratic functions at brainly.com/question/24737967
So, this is a proportion problem. If we express 75% as a fraction (3/4ths), we have:
Since he won all of his games, we add the number won (x), to the number previously won and divide it by the total games played which is just the previous games played plus the number of current games played, so since he lost no games we still add x to the denominator as well. Solving this gives us:
That x value is 20.
We have two points describing the diameter of a circumference, these are:
Recall that the equation for the standard form of a circle is:
Where (h,k) is the coordinate of the center of the circle, to find this coordinate, we find the midpoint of the diameter, that is, the midpoint between points A and B.
For this we use the following equation:
Now, we replace and solve:
The center of the circle is (-8,-7), so:
On the other hand, we must find the radius of the circle, remember that the radius of a circle goes from the center of the circumference to a point on its arc, for this we use the following equation:
In this case, we will solve the delta with the center coordinate and the B coordinate.
Therefore, the equation for the standard form of a circle is:
In conclusion, the equation is the following: