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Find the function y= ax^2 + bx + c whose graph contains the points (1,4), (-2,40), and (2,12).

What is the function?

User Elliot
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1 Answer

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Final answer:

To find the function y = ax^2 + bx + c that passes through the given points, substitute the coordinates into the equation and solve the resulting system of equations. The function is y = 2x^2 - 2x.

Step-by-step explanation:

To find the function y = ax^2 + bx + c that passes through the points (1,4), (-2,40), and (2,12), we can substitute the coordinates of each point into the equation and solve the resulting system of equations.

By substituting the coordinates (1,4), (-2,40), and (2,12) into the equation, we get the following system of equations:

4 = a(1)^2 + b(1) + c

40 = a(-2)^2 + b(-2) + c

12 = a(2)^2 + b(2) + c

Solving this system of equations will give us the values for a, b, and c, and we can then write the equation in the form y = ax^2 + bx + c.

Using the method of substitution or elimination, we can find that a = 2, b = -2, and c = 0. Therefore, the function y = 2x^2 - 2x.

User Ping Li
by
8.1k points

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