I don't have access to the graphs or visual content. However, I can provide you with some general information about the Gateway Arch and help you with some of the questions.
The Gateway Arch is a 630-foot (192 m) monument in St. Louis, Missouri. It is the tallest arch in the world and the tallest man-made monument in the Western Hemisphere. Here are the answers to your questions:
1. The vertex is the highest point on the arch, which is the center or peak of the arch. In the context of the problem, the vertex represents the maximum height or elevation of the arch, which is at the center point.
2. Without knowing the specific question related to "solutions," I cannot answer this question. Please provide more information.
3. To find the quadratic equation in vertex form, we need to use the vertex and another point on the arch. Let's say the vertex is at (0, 630) and another point on the arch is (315, 315). Then we can use the vertex form of the quadratic equation, which is:
y = a(x - h)^2 + k
where (h, k) is the vertex. Plugging in the values, we get:
630 = a(0 - 0)^2 + 630
315 = a(315 - 0)^2 + 630
Solving these two equations simultaneously, we get a = -0.001 and the equation in vertex form is:
y = -0.001x^2 + 630
4. To find the quadratic equation in factored form, we need to use the vertex and another point on the arch. Using the same points as before, we can find the equation in factored form as:
y = a(x - h)(x - p) + k
where (h, k) is the vertex and p is the x-coordinate of the other point. Plugging in the values, we get:
y = a(x - 0)(x - 630) + 630
y = a(x - 315)^2 + 315
Solving these two equations simultaneously, we get a = -0.001 and the equation in factored form is:
y = -0.001(x - 315)^2 + 315
5. Both equations have the same vertex and the same value of a, which means they have the same shape and open downwards. The difference is in the form of the equation, where one is in vertex form and the other is in factored form.
6. The domain of the quadratic equation is all real numbers, as the arch can be any height from 0 to 630 feet.
7. Without knowing the specific location and angle from which the arch is being viewed, I cannot answer this question. Please provide more information.