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V Shaped Parabola
Curves are an important element in design. Curves can be found in everything, from nature to man-made objects. They can be ovals, circles, spirals, or any shape that is not a straight line.
When designing in fashion, cosmetics, or interior design, curves are used to create softer looks and shapes. For example, a soft oval shape is used for lipstick tubes or perfume bottles to create the impression of softness.
Using curves in design is a way to mix up the textures and shapes used. By adding one curve, you can add a new level of softness or pastiness to your shape.
This tutorial will teach you how to draw your own curves using the most basic of shapes: the parabola.
Relation between x and y coordinates
A graph’s relation between x and y coordinates is called the coordinate
plane. Most graphs are plotted in a rectangular plane, also known as a Cartesian plane
after its creator. But some, like the parabola, are plotted in a different kind of plane called a
symmetric axis triangular plane or V-shaped parabola.
Parabolas can be rotated and reflected along any of the axes that define the graph. This is why it is considered a symmetric axis triangular plane. Parabolas can also be shifted vertically or horizontally along any of the axes that define the graph.
Understanding how to rotate, reflect, and shift parabolas will make solving for y-intercepts, finding points of intersection with other curves, and finding length ratios easier. All of these solutions will be explained in this article.
Understanding the curve
The shape of the curve your waistline makes is very important. A narrow V shape is the most desirable, as it shows a lean body and little fat on your body.
Unfortunately, due to the nature of the equation, you can not get this shape without working hard! There is no shortcut to getting this shape.
The wider your V shape, the more fat you have on your body. If you have a very broad shoulder width with a narrow waist, you have achieved the X shaped parabola!
This can be hard to understand until you see it graphically. Many people get frustrated when they can’t lose weight in their waistline, but it may just be because their body shape does not allow for a narrow V shape.
It is important to recognize that this curve is natural for some bodies and not others. Trying to force yourself into a different shape can cause more problems.
x- and y-axis
The parabola uses both the x- and y-axis as its basis. The x-axis is used to determine where the parabola opens and closes, while the y-axis is used to determine how wide or narrow the curve is.
Parabolas can open upwards or downwards, called opening quadrants. These quadrants are labeled with either a ‘+’ or ‘−‘ sign.
A parabola that opens downwards and has a negative opening quadrant is called a descending parabola. This means that as x increases, y decreases. A typical example of this would be an object falling down.
A parabola that opens upwards and has a positive opening quadrant is called an ascending parabola. This means that as x increases, y increases. A typical example of this would be an object being shot up into the air.
The width of the curve is based on the difference between the values of x and y at each point along the curve.
Equation of parabola
A parabola is defined by its equation, which is:
Where a is the value of the coordinate of the vertex (the peak) and f(x) is the function of the variables x. In other words, a is the height of the vertex and f(x) is the length of the line that connects the vertex to the origin (0,0).
The variable x represents any coordinate on either axis. So if x represented a horizontal coordinate, then y would represent a vertical coordinate.
Parabolas can be further defined by their shape: vertical or horizontal. A vertical parabola has a vertical axis of symmetry, which means that if divided the parabola in half, they would be identical. A horizontal parabola has an identical side to an adjacent side- it looks like a rectangle! Both have different properties that affect how they shoot projectiles.
Example of parabola
A parabola is a curve that is typically defined by a single equation. That equation is y=ax²+bx+c, where a is the value of the slope of the line that cuts the parabola in half, b is the starting value, or x-value, of the parabola, c is the ending value, or x-value of the parabosa
Parabolic shapes are seen in many places in nature. Raindrops fall into a parabolic shape, and ocean waves curl into a trough and crest that resemble a symmetrical U-shape. The way water moves down rivers also follows a weakly shaped parabola.
Parabolic flights are used by aircrafts to gain enough momentum to reach higher altitudes. By using a ramp that curves up at the end, the plane ultimately flies up in a parabolic shape to catch more air which gives it more lift.
Applying the parabola
A very popular and sexy shape for curves is the V-shaped parabola. Most frequently seen in hip-fleet cars, the V-shape curve is an elegant way to frame a vehicle.
Vehicles are designed with curves in particular shapes for a reason. Curves can be linear or circular, but all have a specific purpose. Linear curves add stability to the vehicle while circular curves make the vehicle look sleek and fast.
How does one apply this to their life? Well, not literally on your car, but in your life!
By having goals that are set up for success, and achieving small successes that lead up to bigger ones, you will soon find yourself climbing up the ladder of success. It will look like a gradual climb from the ground up, but you will see the lines of progress.
Verifying the equation
Once you have drawn your parabola and have verified that it is a parabola, you can then verify that your parabola has the equation you chose.
To do this, first check that the y-intercept is 0. The y-intercept is where the graph crosses the y-axis, or vertical axis. This must be verified because if it was not a parabola, there would be no value for y when x was zero.
Then, check if the curve is symmetrical by comparing the upper half of the curve to the lower half. If they are identical, then your parabola has found its equation!
Finally, check if the coefficient of x2 is 1.