SOLUTION: Find a+b+c if the graph of the equation y=ax^2+bx+c is a parabola with vertex (5,3), a vertical axis of symmetry, and contains the point (2,0).

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find a+b+c if the graph of the equation y=ax^2+bx+c is a parabola with vertex (5,3), a vertical axis of symmetry, and contains the point (2,0).      Log On


   

Question 1091008: Find a+b+c if the graph of the equation y=ax^2+bx+c is a parabola with vertex (5,3), a vertical axis of symmetry, and contains the point (2,0).
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%28x-5%29%5E2%2B3

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y-3=a%28x-5%29%5E2
%28y-3%29%2F%28x-5%29%5E2=a
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a=%280-3%29%2F%282-5%29%5E2
a=-3%2F%28-3%29%5E2
a=-1%2F3
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y=%28-1%2F3%29%28x-5%29%5E2%2B3
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%28-1%2F3%29%28x%5E2-10x%2B25%29%2B3
%28-1%2F3%29x%5E2%2B%2810%2F3%29x-25%2F3%2B3
%28-1%2F3%29x%5E2%2B%2810%2F3%29x%2B9%2F3-25%2F3
%28-1%2F3%29x%5E2%2B%2810%2F3%29x-16%2F3, in a form decreasing degree of x
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system%28a=-1%2F3%2Cb=10%2F3%2Cc=-16%2F3%29, and you can compute a+b+c.