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batballbat
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how can the graph of the function y=ax^n be obtained from the graph of y=x^n if a is positive?negative
A parabolic function is a type of mathematical function that follows the form y = ax^n, where a is a constant and n is a positive integer. It is called "parabolic" because its graph takes the shape of a parabola, which is a U-shaped curve.
To graph a parabolic function, you can plot a few points on a coordinate plane and then connect them with a smooth curve. Alternatively, you can use the equation y = ax^n to find the coordinates of the vertex (highest or lowest point) and a few other points on the graph, and then plot and connect those points.
The value of a in a parabolic function determines the direction and shape of the graph. If a is positive, the graph will open upwards like a "smile" and if a is negative, the graph will open downwards like a "frown". The magnitude of a also affects the steepness of the curve.
Yes, a parabolic function can have a negative exponent. In this case, the graph will still take the shape of a parabola, but it may be reflected across the x-axis (if n is odd) or across both the x-axis and y-axis (if n is even).
Parabolic functions are commonly used to model the trajectory of objects in projectile motion, such as a ball being thrown or a rocket being launched. They are also used in engineering to design curved structures such as arches and bridges, and in economics to study the relationship between supply and demand.