SOLUTION: What is the quadratic equation whose roots are -1,5 and passes through the point (1,1). Please show your work.

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Question 952421: What is the quadratic equation whose roots are -1,5 and passes through the point (1,1). Please show your work.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
first you are looking for the quadratic equation y=ax%5E2%2Bbx%2Bc
since you are given roots +x%5B1%5D=-1,x%5B2%5D=5, you will use zero product theorem to find equation:
%28x-x%5B1%5D%29%28x-x%5B2%5D%29=0
%28x-%28-1%29%29%28x-5%29=0
%28x%2B1%29%28x-5%29=0
and passes through the point (1,1),so we need a constant c to multiply zero product using given point
y=c%28x%2B1%29%28x-5%29+ ...........now if you sub in x=1 and y=1
1=c%281%2B1%29%281-5%29+
1=c%282%29%28-4%29+
1=-8c

giving c=-%281%2F8%29
and, we have
y=-%281%2F8%29%28x%2B1%29%28x-5%29
y=-%281%2F8%29%28x%5E2-4+x-5%29
y=-%281%2F8%29x%5E2%2Bx%2F2%2B5%2F8