The first step to solving almost any problem is to understand what the question is asking and what is given to us in order for us to solve for the question. In this problem, we are given a graph and asked two questions. One being what the coordinates of the vertex are and whether this parabola has a maximum or a minimum.
Let's define what a vertex, maximum, and minimums are.
- Vertex ⇒ Vertex is the point at which it either reaches the maximum or minimum. This point can be easily defined as where the slope becomes flat.
- Maximum ⇒ Maximum occurs when the vertex is at the top and the lines go down in a negative-y-direction. Therefore with the vertex being at the top that would be considered a maximum as it's the largest point in the graph.
- Minimum ⇒ Minimum occurs when the vertex is at the bottom and the lines go up in a positive-y-direction. Therefore with the vertex being at the bottom that would be considered a minimum as it's the smallest point in the graph.
Now, looking at our problem we can see that our vertex is at the bottom therefore it would classify as a minimum. Now that we know we have a minimum vertex, let us determine what the actual coordinates of the vertex are.
We can see that we travel -3 in the x direction and -5 in the y direction which means that the coordinate for our vertex is (-3, -5) where the first number represents the x-value and the second number represents the y-value.
