Find an equation of a parabola that has curvature 10 at the origin. (Assume the parabola has its vertex at the origin, and opens upward.)

Step-by-step explanation:

The equation of a parabola is:

We know that the vertex is at the vertex, so b and c are 0.

Then, our quadratic equation is rewritten as:

  (1)

Now, the equation of the curvature related to a function is given by:

 (2)

Here:

y'' is the second derivative of the function

y' is the first equation of the function

κ is the curvature

Let's find the first and the second derivative of y whit respect to x.

Putting these values in equation (2), we have:

We can evaluate the curvature at the origin to find the parameter a. Which means x=0. (Let's recall that κ = 10 at the origin)

Now, we have two options for the equation:

or

But we know that this parabola opens upward, so the value of a must be positive.

Therefore, the equation is:

I hope it helps you!

it is true

step-by-step explanation:

all the combinations add up i used   calculator