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

Algebra ->  College  -> Linear Algebra -> 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      Log On


   

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) About Me  (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) About Me  (Show Source):
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since (1,3) and (2,3) share a y-value, they are on opposite sides of the vertex.
The x coordinate of the vertex is %281%2B2%29%2F2=3%2F2
Use the vertex form,
y=a%28x-h%29%5E2%2Bk
y=a%28x-3%2F2%29%5E2%2Bk
Use your points to solve for a and k.
3=a%281-3%2F2%29%5E2%2Bk
3=a%281%2F4%29%2Bk
1.a%2B4k=12
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.
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5=a%283-3%2F2%29%5E2%2Bk
5=a%289%2F4%29%2Bk
2.9a%2B4k=20
Subtract eq. 1 from eq. 2,
9a%2B4k-a-4k=20-12
8a=8
highlight_green%28a=1%29
Then use either equation to solve for k.
1%2B4k=12
4k=11
highlight_green%28k=11%2F4%29
.
.
y=a%28x-3%2F2%29%5E2%2Bk
y=%28x-3%2F2%29%5E2%2B11%2F4
y=%28x%5E2-3x%2B9%2F4%29%2B11%2F4
highlight%28y=x%5E2-3x%2B5%29
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.
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