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Jul 12, 2021 · For most of the graph theory we cover in this course, we will only consider simple graphs. However, there are some results for which the proof is identical whether or not the graph is simple, and other results that actually become easier to prove if we allow multigraphs and/or loops, than if we only allow simple graphs.
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A 2D or two-dimensional figure is a figure or shape that we can represent in two dimensions or on paper. Some 2-D shapes include circle, square, rectangle, and triangle. The vertex of a 2D figure is the point of intersection of two sides of the shape. The two sides of the shape or figure meet to form an angle, and thus a vertex is formed.
- How many vertices does a cone have?A cone has a single vertex. There is only one point on the cone where its surface meets and forms an angle. Hence, only a single vertex forms in a...
- How many vertices does a cube have?A cube has eight vertices. A cube is a three-dimensional object with six faces, twelve edges, and eight vertices.
- Which objects do not have a vertex?Any object with no straight edges or angles formed by edges does not have a vertex. Examples of objects without a vertex are circles, cylinders, an...
- How many vertices does a tetrahedron have?A tetrahedron has four vertices. It also has six edges and four triangular faces.
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 coefficient of a and get y = ax^2 -2ahx +ah^2 + k. This is standard form of a quadratic equation, with the normal a, b and c in ax^2 + bx + c equaling a, -2ah and ah^2 + k, respectively. 1 comment.
- 3 min
- Sal Khan
- How do you convert a "vertex form" equation into "standard form" equation?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...
- in the graph why did you use 1 and 3 as random numbers?You could have used whatever you wanted, but 1 and 3 were convenient as they produced whole numbers when plugged into the equation.
- What if the a value is a fraction? How would I simply graph two coordinates that aren’t the vertex?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...
- Where did you get the two in the (2,5)?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...
- how would we find the y intercept of an equation in vertex form?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...
- What if A is a fraction? Like; -1/3(x+2)^2 + 3Well, 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 +...
- Ok. So why does the equation y= -2(x-2)^2+5 have a vertex (h,k) of (2,5) if the value of h is -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...
- We can't make a fully accurate parabola by hand, could we ?Well, mathematically speaking, there is no way to draw a "perfect" parabola by hand. Think of it like drawing a "perfect" circle.
- What if the first number is a fractionIt does not change the process if the first number is a fraction.
- At 1:25, how does he determine that the maximum value for y is (2,5)? Is k always the y term, and is...y=a(x-h)²+k I already told you about k which is the vertical shift and (x-h)² which is the horizontal shift on your other question. Now I will tell...
Answer: The vertex of a dodecagon is the point at which twelve sides meet. Summary. In this article, we discussed the vertex definition in geometry. A vertex is a point or corner where two or more lines meet, and it is usually labeled with uppercase letters. A vertex can be described by its location, angle, length, and type.
For standard form: y=Ax^2+Bx+CLook at the coefficient of the x^2 term. If "A" is positive, the parabola opens up. If "A" is negative, then the parabola opens down.For Vertex Form: y=a (x-h)^2+kThe sign of "a" determines the direction of the parabola. If "a" is positive, the parabola opens up.
