SOLUTION: Let a, b>0. Find the equation of the parabola y = ax2 + bx + y that passes through the points (-a,0), (0, b), and (a, 0)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Let a, b>0. Find the equation of the parabola y = ax2 + bx + y that passes through the points (-a,0), (0, b), and (a, 0)      Log On


   

Question 314318: Let a, b>0. Find the equation of the parabola y = ax2 + bx + y that passes through the points (-a,0), (0, b), and (a, 0)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since it has zeros at x=0+%2B-+a then
f%28x%29=C%28x-a%29%28x%2Ba%29 where C is a constant.
We can determine C when x=0
f%280%29=C%280-a%29%280%2Ba%29=b
C%28-a%5E2%29=b
C=-b%2Fa%5E2
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f%28x%29=C%28x%5E2-a%5E2%29
f%28x%29=-%28b%2Fa%5E2%29%2A%28x%5E2-a%5E2%29
f%28x%29=b-x%5E2%28b%2Fa%5E2%29