Final answer:
The graph reflection, maximum or minimum, increasing and decreasing intervals, vertex form equation, domain, and range of the given graph are explained.
Step-by-step explanation:
The given question asks about various aspects of a graph. Let's break down each part:
- Is the graph reflected? Explain: To determine if the graph is reflected, we need to check if the function has a negative sign in front of it. If it does, the graph is indeed reflected.
- Does it have a maximum or a minimum? What is it? To find a maximum or minimum on a graph, we look for the highest or lowest point on the graph, respectively. The vertex of the graph represents the maximum or minimum value, and its coordinates are the x and y values at that point.
- What is the increasing interval? The increasing interval is the range of x-values over which the graph is increasing. In other words, it is the range of x-values that correspond to a positive slope.
- What is the decreasing interval? The decreasing interval is the range of x-values over which the graph is decreasing. In other words, it is the range of x-values that correspond to a negative slope.
- Write an equation in vertex form for this graph. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h,k) represents the coordinates of the vertex. To write the equation in vertex form, we need to know the coordinates of the vertex.
- What's the domain? The domain of a function represents all the possible x-values that the function can take. To determine the domain, we look at the x-values for which the graph is defined.
- What's the range? The range of a function represents all the possible y-values that the function can take. To determine the range, we look at the y-values for which the graph is defined.