SOLUTION: find the equation of the parabola that passes through the point (6,10) and has a vertex at (4,3)
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Question 528644: find the equation of the parabola that passes through the point (6,10) and has a vertex at (4,3)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Presuming a vertical axis of symmetry, if the vertex has an 
-coordinate of 4, then a point 2 units to the left of the vertex will have the same function value as a point 2 units to the right of the vertex. Hence )
has to be on the parabola. Now that we have three non-collinear points we can uniquely determine the parabola.
A parabola with a vertical axis of symmetry has an equation of the form:
Given the point (4,3):
^2\ +\ b(4)\ +\ c\ =\ 3)
Given the point (6,10)
^2\ +\ b(6)\ +\ c\ =\ 10)
Given the point (2,10)
^2\ +\ b(2)\ +\ c\ =\ 10)
Solve the 3X3 linear system to obtain the desired coefficients.
John
My calculator said it, I believe it, that settles it
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