SOLUTION: Hi! I need to determine the equation of a parabola in the form y-k=a(x-h)^2 I am given 2 points on the graph (0,6) and (14,0) I am given Part of V (9,k) I have tried so many

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Hi! I need to determine the equation of a parabola in the form y-k=a(x-h)^2 I am given 2 points on the graph (0,6) and (14,0) I am given Part of V (9,k) I have tried so many      Log On


   

Question 171023: Hi! I need to determine the equation of a parabola in the form y-k=a(x-h)^2
I am given 2 points on the graph (0,6) and (14,0)
I am given Part of V (9,k)
I have tried so many things, but nothing is even close to what it should be and I am ending up just writing the question over and over and now I am fully frustrated. I know I have to use both points given in order to get "a" and "k" and I probably have to substitute or eliminate but with two unknowns I have no idea how to go about it!
Any help would be seriously appreciated!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
determine the equation of a parabola in the form y-k=a(x-h)^2
I am given 2 points on the graph (0,6) and (14,0)
I am given Part of V (9,k); I assume this means h=9
;
Two equations:
:
0,6:
6 - k = a(0 - 9)^2
6 - k = 81a
or
81a + k = 6
:
14, 0
0 - k = a(14-9)^2
0 - k = a(5)^2
25a + k = 0
;
Eliminate k, find a
81a + k = 6
24a + k = 0
-------------subtraction eliminates k
56a = 6
a = 6%2F56
a = 3%2F28
:
Find k using 25a + k = 0
25*(3%2F28) + k = 0
75%2F28 + k = 0
k = -75%2F28
:
The equation:
y = 3%2F28(x - 9)^2 - 75%2F28
:
Plots this:

:
Looks about right