SOLUTION: How would i write a function of the form y=ax^2+bx whose graph contains the points (1,6) and (3,6)?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: How would i write a function of the form y=ax^2+bx whose graph contains the points (1,6) and (3,6)?      Log On


   

Question 366132: How would i write a function of the form y=ax^2+bx whose graph contains the points (1,6) and (3,6)?
Found 2 solutions by solver91311, Fombitz:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Remember that the points are ordered pairs of the form

So if is an element of the solution set of , then



must be a true statement.

Similarly,



must also be a true statement.

Solve the two variable linear system for and to get the specific coefficients for .

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
By solving for a and b using the two points provided.
y=ax%5E2%2Bbx
6=a%281%29%5E2%2Bb%281%29
1.a%2Bb=6
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.
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6=a%283%29%5E2%2Bb%283%29
6=9a%2B3b
2.3a%2Bb=2
Subtract eq. 1 from eq. 2,
3a%2Bb-a-b=2-6
2a=-4
highlight%28a=-2%29
Then from eq. 1,
-2%2Bb=6
highlight%28b=8%29
.
.
.
highlight%28y=-2x%5E2%2B8x%29
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