Calculus quadratic function

algray09

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I’m confused how to set up the quadratic equation, I know that I have to use the data at t=1,8, and 15 but the area for each point is 15,35, and 68. So I’m thinking 15, 35, and 68 have to be in the equation but I don’t know how many variable there should be and degrees.
 

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Subhotosh Khan

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I’m confused how to set up the quadratic equation, I know that I have to use the data at t=1,8, and 15 but the area for each point is 15,35, and 68. So I’m thinking 15, 35, and 68 have to be in the equation but I don’t know how many variable there should be and degrees.
In this Quadratic equation there is one independent variable (t or x) and one dependent variable (A or y).

What is the degree of Quadratic polynomial ?
 

algray09

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See that’s what I don’t know because I know the numbers I’m supposed to use because of the table. Somehow the quadratic equation is supposed to represent the area of a circle but is not the area of circle equation.
 

blamocur

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See that’s what I don’t know because I know the numbers I’m supposed to use because of the table. Somehow the quadratic equation is supposed to represent the area of a circle but is not the area of circle equation.
You don't know the degree of a quadratic equation? Do you know why they call them "quadratic"?

Also, I wouldn't worry about circle equation, which is just a part of a story but is not really related to the problem at hand: given 3 values of Y for 3 values of X express Y as a quadratic function of X.
 

algray09

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No I know what a degree is but I don’t know for this equation like is the first coefficient in this equation x^2. It wants the data from those points so I’m assuming the number values in the equation are 15, 35, and 68. Would it be 15x^2 + 35x +68?
 

algray09

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No I know what a degree is but I don’t know for this equation like is the first coefficient in this equation x^2. It wants the data from those points so I’m assuming the number values in the equation are 15, 35, and 68. Would it be 15x^2 + 35x +68?
Though it wants quadratic function so using the data from 1,8, 15 would it be f(x)=15x^2 + 35x +68
 

JeffM

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First of all, thank you for giving us the entire problem. That helps us help you.

Second, it should be obvious from inspection that the function cannot be an exact quadratic. However, there is reason to believe that a quadratic could be an appropriate approximation, and the graph of the data confirms that. So this is an exercise in approximation.

Third, I am guessing that you are studying quadratic equations. What is the general formula for a quadratic equation?
 

algray09

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Standard form it’s ax^2+bx+c do I have to make 3 equations then and solve for each variable
A(1)^2+b(1)+c=15
A(8)^2+b(8)+c=35
A(15)^2+b(15)+c=68
 

algray09

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So I got my equation which I have attached to this. Now for part B I’m assuming I plug in 16 for x into that equation
 

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