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Question

One type of generic mouth guard is made from plastic. It is wide and long, enabling you to cut ends off so that it does not extend past your back teeth. To shape it to your mouth, you put it into hot water, which softens the plastic so that it can be shaped to the teeth. This will allow it yo shrink, to fit almost any mouth. When creating a mouth guard like this one, how would you alter the equation of your parabola? Justify your answer with clear explanations.

Answer 1

Hey Soham N.,

In order to have a mouth guard fit into your mouth you’d obviously have to make it narrower. When it comes to a parabola, you would have to alter the number of the quadratic coefficient because the greater the quadratic coefficient the narrower the parabola will get. Thus, enabling the parabola shaped mouth guard to fit properly into your mouth.

Example: A parabola with the equation 3x^2 + 2x - 4 would make a parabola more narrow than a parabola with an equation of x^2 +2x - 4 because the quadratic coefficient of the first equation is larger then the second equation.

3 > 1

side note:

ax^2 + bx + c is the formula, with (a) representing the quadratic coefficient. The higher the coefficient the more narrow the parabola will get.

Let’s do this! :)