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mojki1
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Find all the pairs (x, y)R^2, throught which does not cross any curve : y = - x^2 + (4-2p)x + p^2 . Finding pairs (x,y) are the co-ordinate points . Thanks for help
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A parabola is a symmetrical curve that can be found in nature, as well as in mathematical equations. It is typically in the shape of a U or an upside-down U and is formed by the graph of a quadratic function.
To find (x,y) pairs without crossing the curve, you can use the formula y = ax^2 + bx + c, where a, b, and c are constants. Plug in different values for x and solve for y to get the (x,y) pairs. You can also use a graphing calculator or a graphing software to plot the points and draw the parabola without crossing it.
The key features of a parabola include the vertex, which is the highest or lowest point on the curve, the axis of symmetry, which is a vertical line that divides the parabola into two symmetrical halves, and the x-intercepts, which are the points where the parabola crosses the x-axis. The coefficient a determines the direction and width of the parabola, while the constant c shifts the parabola up or down on the y-axis.
Finding (x,y) pairs without crossing the curve is important for accurately graphing a parabola and solving problems involving parabolas. It allows us to understand the behavior of the parabola and make predictions based on its properties. It is also an essential concept in higher-level math and physics courses.
Parabolas have many real-life applications, such as in architecture, where they are used to design arches and bridges. They are also used in physics to model the trajectory of a projectile, such as a ball being thrown or a rocket being launched. In economics, parabolas are used to represent cost and revenue functions. Additionally, parabolas can be seen in nature, such as the shape of a water fountain or the flight path of a bird.