Question 1150746: A parabola with equation y = x^2 + bx + c passes through the points (2,3) and (4,3). What is c?
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
The parabola has the same "level'"/values of "y" at x= 2 and x= 4;
hence. the symmetry line is x= 3, and the parabola has the vertex form
y =  .
At x= 2, we have 3 =  = 1 + c; hence, in this vertex form, c= 2.
In the "general form equation"
y = x^2 - 6x + 9 + 2 = x^2 - 6x + 11, c = 11. ANSWER
Answer by Edwin McCravy(20060)  (Show Source):
You can put this solution on YOUR website!
Substitute (x,y) = (2,3) in
y = x^2 + bx + c
3 = 2^2 + b(2) + c
3 = 4 + 2b + c
-1 = 2b + c
2b + c = -1
Substitute (x,y) = (4,3) in
y = x^2 + bx + c
3 = 4^2 + b(4) + c
3 = 16 + 4b + c
-13 = 4b + c
4b + c = -13
Solve this system:
and get b = -6, c = 11
Edwin
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