SOLUTION: Find the equation of the parabola passing through the given points (1,3)(2,3)(3,5). Show the system of equations containing the 3 points and then solve for the constants, a,b,and c

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Question 358553: Find the equation of the parabola passing through the given points (1,3)(2,3)(3,5). Show the system of equations containing the 3 points and then solve for the constants, a,b,and c. Then, show the standard form equation of the parabola.
Found 3 solutions by ewatrrr, Alan3354, Fombitz:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!


Hi,

Pt(1,3) and Pt(2,3) tell us they could not satisfy an equation for a parabola.

Each x values does not have an unique y value.



 

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
 



 

Answer by Fombitz(32388)   (Show Source): You can put this solution on YOUR website!
 Since (,) and (,) share a y-value, they are on opposite sides of the vertex.

The  coordinate of the vertex is 

Use the vertex form,





Use your points to solve for  and .





1.

.

.

.





2.

Subtract eq. 1 from eq. 2,







Then use either equation to solve for .







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.

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