Mathematics, 28.10.2020 16:40 taylorbohr6823

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.)

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Answer from: rhd112458

An equation of a parabola that has curvature 6 at the origin is $\rm f(x) = 3x^2$ .

We have to determine

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

What is the equation of a parabola that has a curvature at the origin?

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

$\rm f(x) = ax^2$

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

$\rm k(0) = 2a\\\\6 = 2a\\\\a = \dfrac{6}{2}\\\\a=3$

Therefore,

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

$\rm f(x) = ax^2$

$\rm f(x) = 3x^2$

Hence, an equation of a parabola that has curvature 6 at the origin is $\rm f(x) = 3x^2$ .

To know more about Parabola click the link given below.

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Answer from: ashleyrover11

The equation of a parabola that has a curvature 6 at the origin is $f(x) = 3\cdot x^{2}$ .

Step-by-step explanation:

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

$f(x) = a\cdot x^{2}+b\cdot x + c$ (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:

$K = \frac{\left|\frac{d^{2}y}{dx^{2}} \right|}{\left[1+\left(\frac{dy}{dx} \right)^{2}\right]^{\frac{3}{2} }}$ (Eq. 2)

Where $\frac{dy}{dx}$ and $\frac{d^{2}y}{dx^{2}}$ are the first and second derivatives of the function, respectively. Each expression is described below:

$\frac{dy}{dx} = 2\cdot a\cdot x + b$

$\frac{d^{2}y}{dx^{2}} = 2\cdot a$

If we know that a 0 , b = c = 0 , x = 0 and K = 6 , then the equation of curvature and polynomial are, respectively:

$\frac{2\cdot a}{1^{\frac{3}{2} }} = 6$

a = 3

The equation of a parabola that has a curvature 6 at the origin is $f(x) = 3\cdot x^{2}$ .

Answer from: Quest

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step-by-step explanation:

Answer from: Quest

each side has a different length.

step-by-step explanation:

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