<PRE><B>Question 1189357</B>
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The solution from the other tutor is fine... but he went to a lot of trouble to find the equation of the parabola from his original three equations.&lt;br&gt;
y=ax^2+bx+c&lt;br&gt;
(1,1): a+b+c=1 [1]
(2,2): 4a+2b+c=2 [2]
(-1,5): a-b+c=5 [3]&lt;br&gt;
Observe that the coefficients of a and b in [1] and [3] are the same.  So subtracting one of those equations from the other will immediately give us b.&lt;br&gt;
2b=-4
b=-2&lt;br&gt;
Now substitute b=-2 in [1] and [2]:&lt;br&gt;
a-2+c=1; a+c=3
4a-4+c=2; 4a+c=6
3a=3
a=1&lt;br&gt;
Substitute a=1 and b=-2 in [1] to find c:&lt;br&gt;
1-2+c=1; c=2&lt;br&gt;
We have a=1, b=-2, c=2.&lt;br&gt;
ANSWER: y=x^2-2x+2 -- which is equivalent to answer choice a&lt;br&gt;
Of course, if this were a question on a multiple choice test, you would simply eliminate answer choices b and c because they contain y^2 terms instead of x^2 terms (making them equations of parabolas with axis parallel to the x-axis).  Then you would simply substitute the coordinates of the given points to determine which of answer choices a and d is correct.&lt;br&gt;
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