SOLUTION: PLEASE help me! I need to write an equation in vertex form when I know the vertex and some points. 1.vertex (0,-1) and (1,1) (-1,1) 2.vertex (2,4) and (1,1) (3,1) 3.verte

Algebra ->  Rational-functions -> SOLUTION: PLEASE help me! I need to write an equation in vertex form when I know the vertex and some points. 1.vertex (0,-1) and (1,1) (-1,1) 2.vertex (2,4) and (1,1) (3,1) 3.verte      Log On


   



Question 609613: PLEASE help me! I need to write an equation in vertex form when I know the vertex and some points.
1.vertex (0,-1) and (1,1) (-1,1)
2.vertex (2,4) and (1,1) (3,1)
3.vertex is (-3,-3) and (2,4) (-8,4)
Thank you so much!!

Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 
Hi
Using the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex
1.vertex (0,-1) and (1,1) (-1,1)
y = ax^2 - 1
1 = a· 1 - 1
2 = a and y = 2x^2 -1
2.vertex (2,4) and (1,1) (3,1)
y = a(x-2)^2 +4
1 = a(3-2)^2 + 4
-3 = a and y = -3(x-2)^2 +4
3.vertex is (-3,-3) and (2,4) (-8,4)
y = a(x+3)^2 -3
4 = a(2 +3)^2 - 3
7/25 = a and y = 7/25(x+3)^2 -3


Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


The standard (or general) form of a parabola is



Given that (2,4) is on the parabola,



Given that (1,1) is on the parabola,



and

Given that (3,1) is on the parabola,



Giving us the 3X3 system








Verification of the solution set element is left as an exercise for the student.

Hence the standard (or general, if you like) form of the equation is:



Complete the square to find vertex form:







John

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