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 .

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Step-by-step explanation: