When the quadratic function f𝑓 is graphed in the xy𝑥𝑦-plane, where y=f(x)𝑦=𝑓(𝑥), its vertex is (5,3).(5,3). One of the x𝑥-intercepts of this graph is (375,0)(375,0). What is the other x𝑥-intercept of this graph?

The vertex form of a quadratic function is given by f(x) = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. Given that the vertex is (5,3), we can substitute these values into the equation to get f(x) = a(x-5)^2 + 3.

We also know that one of the x-intercepts is (375,0). An x-intercept is a point where the graph crosses the x-axis, so the y-coordinate is 0. We can substitute these values into the equation to find the value of a:

0 = a(375-5)^2 + 3 -3 = a(370)^2 a = -3 / (370)^2

Now that we have the value of a, we can write the complete equation of the function as f(x) = -3/(370)^2 * (x-5)^2 + 3.

The x-intercepts of the graph are the values of x for which f(x) = 0. We already know one of these values is 375. Because the graph of a quadratic function is symmetric about the line x = h, the other x-intercept is the same distance from the vertex as 375, but in the opposite direction.

The distance from the vertex (5,3) to the known x-intercept (375,0) is 375 - 5 = 370. So, the other x-intercept is 5 - 370 = -365. Therefore, the other x-intercept of the graph is (-365, 0).