SOLUTION: A quadratic function in the form of y = ax^2+ bx + 9 has x-intercepts at x = -3 and x = 1. What are the values for a and b?

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Question 1180425: A quadratic function in the form of y = ax^2+ bx + 9 has x-intercepts at x = -3 and x = 1. What are the values for a and b?
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52754)   (Show Source): You can put this solution on YOUR website!
.

According to Vieta's theorem, the product of the roots (-3) and 1 is equal to   :

    (-3)*1 = .

It gives  a =  = -3.



According to Vieta's theorem (again), the sum of the roots (-3) and 1 is equal to  : 

    (-3 + 1) = ,  or

       -2 = ,


which gives  -b = (-2)*(-3) = 6,  or  b = -6.



ANSWER.  a = -3;  b = -6.



Answer by josgarithmetic(39613)   (Show Source): You can put this solution on YOUR website!
Very simple algebra only,


Comparing the terms,



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