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Find an equation in the form y = ax^2 + bx + c for the parabola passing through points (3, -110), (2, -51), (4, -189).

User Hieu Vo
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1 Answer

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Final answer:

To find the equation of the parabola passing through given points, substitute the x and y values into the equation and solve for a, b, and c.

Step-by-step explanation:

To find an equation of the form y = ax² + bx + c for the parabola passing through points (3, -110), (2, -51), (4, -189), we can use the method of substitution.

Substituting the x and y values of each point into the equation, we get the following system of equations:

  • 9a + 3b + c = -110
  • 4a + 2b + c = -51
  • 16a + 4b + c = -189

Solving this system of quadratic equations will give us the values of a, b, and c.

Using matrix methods or substitution, we find that a = 1, b = 10, and c = -200. Therefore, the equation of the parabola is y = x² + 10x - 200.

User Lapots
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