What is an equation to make a parabola (solar cooker)

For math class, we have to build a solar cooker and in order to do that we need an equation that makes a parabola. The solar cooker can't be more than 1 meters in length and width. Any help in making an equation is greatly appreciated.

Lauren,

I believe the answer you are looking for is -

y= (x^2)/(4f)

This equation:

1) Represents a parabola that is symmetric about the y - axis.

2) Has a focal point which occurs at (0 , f)

For example -

1) the equation y = x^2, has a focal point at (0 , 1/4)

2) the equation y= (x^2)*(8) has a focal point at (0, 1/32)

3) the equation y= (x^2)*(1/18) has a focal point at (0, 9)

...

There are actually a couple of problems to consider regarding your restrictions. They include -

1) 1 meter length and width. - If we consider the fact that the width restriction is going to be the variable 'x' times 2 we can modify the equation to -

y = ( (w/2)^2)/(4f)

or

y = (w^2)/(16f)

- 'w' represents the width of the solar cooker, and 'f' is the focal point where the food is cooked. Let's go ahead and plug in the width of 1 meter since we know you want to take advantage of as much sunlight as possible...

Keep in mind that we are not finding an equation at this point, but are just finding some restrictions around the equation, in order to help narrow down some of the solutions.

y = 1/(16f)

or

y = 1/(16f)

What this equation shows us is that:

All parabolas with a total width of '1' (x=1/2) has a height equal to the inverse of 16 times the focal point.

SOooooooo...

Option 1 (A): If you want a focal point of 1 meter ( Where you typically put a skewer for food) you would also have a parabola height of 1/16 meter. (Good option, but on the boarder of being too high because of the skewer) Equation y = (x^2)/4