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Jul 12, 2021 · Definitions: Graph, Vertex, and Edge. A graph \(G\) consists of two sets: \(V\), whose elements are referred to as the vertices of \(G\) (the singular of vertices is vertex); and \(E\), whose elements are unordered pairs from \(V\) (i.e., \(E ⊆ \{\{v_1, v_2\} | v_1, v_2 ∈ V \}\)). The elements of \(E\) are referred to as the edges of \(G\).
The dots are called vertices; an individual dot is a vertex, which is one object of a set of objects, some of which may be connected. We often label vertices with letters. For example, Graph G has vertices a, b, c, and d, and Multigraph H has vertices, e, f, g, and h. Each line segment or connection joining two vertices is referred to as an edge.
Try to graph y=x² (|a| =1) and then y=2x² (|a| > 1) and y=(1/2)x² ( |a| < 1) you will what I mean about skinny and fat parabola. About the vertex, the vertex is determined by (x-h)² and k. The x value that makes x-h=0 will be the x-coordinate of the vertex. K will be the y-coordinate of the vertex. y=-10(x+4)²-3
- 3 min
- Sal Khan
- y = a(x-h)^2 + k is the vertex form equation. Now expand the square and simplify. You should get y = a(x^2 -2hx + h^2) + k. Multiply by the coeffic...
- You could have used whatever you wanted, but 1 and 3 were convenient as they produced whole numbers when plugged into the equation.
- It is not possible to graph a parabola with only 2 points that are not a vertex, unless you also have the average rate of change or both points are...
- It took me 15 minutes to understand this but ,, >> as you can see , just substitute the value by this a(x-h)^2 + k -2(x-2)^2 + 5 Here Sal has taken...
- For any equation, you can find the y-intercept by using x=0 in the equation. For example: y=2(x+3)^2-4 Set x=0: y=2(0+3)^2-4 = 2(9)-4 = 18-4 = 14 S...
- Well, the best way to graph this is to first convert this into standard form. We expand the square and combine any like terms: f(x) = -1/3(x+2)^2 +...
- That is because the vertex form is: y = a(x - h)² + k In this case a = -2 k = 5 h must be 2 because the original form states -h. Therefore, we have...
- Well, mathematically speaking, there is no way to draw a "perfect" parabola by hand. Think of it like drawing a "perfect" circle.
- It does not change the process if the first number is a fraction.
Learning Outcomes. Identify the vertices, edges, and loops of a graph. Identify the degree of a vertex. Identify and draw both a path and a circuit through a graph. Determine whether a graph is connected or disconnected. Find the shortest path through a graph using Dijkstra’s Algorithm.
Check out this video. Example 1: Vertex form. Graph the equation. y = − 2 ( x + 5) 2 + 4. This equation is in vertex form. y = a ( x − h) 2 + k. This form reveals the vertex, ( h, k) , which in our case is ( − 5, 4) . It also reveals whether the parabola opens up or down. Since a = − 2 , the parabola opens downward.
- Do some more Khan Academy videos and exercises. You'll get the hang of it sooner of later if you try! Good luck!
- One way is to complete the square and put in vertex form, Another way is to use -b/2a as the x coordinate and then use that to solve for y.
- It comes from the Latin word quadratum, which means square.
- Yes, the more points you plot, the more accurate you can draw the curve. Some turn the graph paper sideways and draw on one side of the vertex, rot...
- If you know the vertex and another point, then you also know the reflexive point, so you have 3 points. So two points work as long as one of them i...
- Yes, don't skip it. Try to understand it, and it will save you a lot of frustration later on.
- Sal has the equation: y = -2(x+5)^2+4. This is vertex form. So, you graph the vertex and then find points to the left and right of the vertex. When...
- On Example 1, the vertex was at (-5,4). Sal moved over 1 unit to pick x=-4. I believe he did this to demonstrate the impact of the -2 in front. It...
Learning Outcomes. Identify the vertices, edges, and loops of a graph. Identify the degree of a vertex. Identify and draw both a path and a circuit through a graph. Determine whether a graph is connected or disconnected. Find the shortest path through a graph using Dijkstra’s Algorithm.
In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of ...
