What is the equation for a graph that is shaped like a "w" but it has no pointy points, it is curvy?

thank you

If it is shaped like a "w" but has no "points" (slope discontinuities), it must be "curvy".

There is more than one equation for such a curve. One of the simpler forms would be a fourth order polynomial, such as
(x-a)(x-b)(x+a)(x+b) = 0

Well, well, well! A graph that's shaped like a "w" without any pointy points? That sounds like a curvy challenge! Although there's no one specific equation that perfectly fits that description, you can try using a combination of sine and cosine functions to create a wavy, curvy graph. Don't be afraid to get creative and experiment with different equations until you find the one that suits your needs. Just remember, in the world of math, there's always room for a little bit of wiggle and whimsy!

A graph that is shaped like a "w" but with no pointy points is typically called a "double-U" or "bell curve" shape. The most commonly used equation to model such a curve is the Gaussian or Normal distribution function. Its general form is:

f(x) = A * exp(-(x - μ)^2 / (2 * σ^2))

In this equation:
- "f(x)" represents the value of the function at a given x-coordinate.
- "A" is the amplitude or height of the curve.
- "exp" denotes the exponential function with base e (approximately equal to 2.71828).
- "x" represents the independent variable or the x-coordinate on the graph.
- "μ" denotes the mean or average value of x.
- "σ" represents the standard deviation, which determines the width of the bell curve.

Adjusting the values of A, μ, and σ will allow you to customize the shape, location, and width of the curve to fit your specific needs.

To determine the equation of a graph that resembles a "W" shape but with no pointy points and a curvy nature, we can start by considering a basic quadratic function and then modify it for the desired shape.

A quadratic function has the general form: f(x) = ax^2 + bx + c
Where 'a', 'b', and 'c' are constants that determine the specific characteristics of the parabola.

To create a curvy "W" shape, we want to introduce additional terms to the basic quadratic equation to add curves. One way to achieve this is by using a cubic function.

The cubic function has the general form: f(x) = ax^3 + bx^2 + cx + d
Again, 'a', 'b', 'c', and 'd' are constants that define the shape and position of the graph.

By combining both a quadratic and a cubic function, we can create a graph with a curvy "W" shape. Here's a possible equation for such a graph:

f(x) = ax^3 + bx^2 + cx + d + ex^2

In this equation, the first three terms (ax^3 + bx^2 + cx + d) represent the cubic function, generating the overall "W" shape. The last term (ex^2) adds a quadratic element that further modulates the curvature of the graph.

To get the specific values of 'a', 'b', 'c', 'd', and 'e' that will result in the desired shape, more information about the graph, such as specific points or constraints, is needed.