SOLUTION: A parabola with the equation of the form y = ax^2 + bx + c has the point (3, 1) as its vertex. If (1, 3) also lies on the parabola, which of the following is another point on this

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: A parabola with the equation of the form y = ax^2 + bx + c has the point (3, 1) as its vertex. If (1, 3) also lies on the parabola, which of the following is another point on this      Log On


   

Question 343971: A parabola with the equation of the form y = ax^2 + bx + c has the point (3, 1) as its vertex. If (1, 3) also lies on the parabola, which of the following is another point on this parabola?
(A)(-3, -1) (B) (-1,-3) (C) (2, 2)(D) (2, 6) (E) (5, 3)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
In vertex form,
y=a%28x-3%29%5E2%2B1
Using (1,3),
3=a%281-3%29%5E2%2B1
a%28-2%29%5E2=2
4a=2
a=1%2F2
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highlight_green%28y=%28x-3%29%5E2%2F2%2B1%29
Now that you have the equation, test all of the points.
I'll do one, you do the remaining four.
A) (-3,-1):-1=%28-3-3%29%5E2%2F2%2B1
-1=%28-6%29%5E2%2F2%2B1
-1=36%2F2%2B1
-1=18%2B1
-1=19
False, so (-3,-1) is not a point on the parabola.
Continue with the remaining points in the same manner.
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