Find an equation of a parabola that has curvature 6 at the origin. (Assume the parabola has its vertex at the origin, and opens upward.)

An equation of a parabola that has curvature 6 at the origin is .

We have to determine

An equation of a parabola that has curvature 6 at the origin.

The equation of a parabola that has a curvature a at the origin is;

The value of a is given by k(0) = 8;

Therefore,

The equation of a parabola that has a curvature a at the origin is;

Hence, an equation of a parabola that has curvature 6 at the origin is .

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The equation of a parabola that has a curvature 6 at the origin is .

Step-by-step explanation:

All parabolas are represented by second-order polynomials, whose standard form is:

(Eq. 1)

Where:

- Independent variable, dimensionless.

- Dependent variable, dimensionless.

, , - Coefficient of the parabola, dimensionless.

From Vectorial Calculus we know that curvature (), dimensionless, is defined by the following expression:

(Eq. 2)

Where and are the first and second derivatives of the function, respectively. Each expression is described below:

If we know that , , and , then the equation of curvature and polynomial are, respectively:

The equation of a parabola that has a curvature 6 at the origin is .

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

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