SOLUTION: Find the equation of parabola with the given condition: Axis vertical and passing through (0,0)(1,0) and (5,-20) Note: Do not use y=ax^2+bx+c as the equation Use: (x-h)^2=-4a(

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Find the equation of parabola with the given condition: Axis vertical and passing through (0,0)(1,0) and (5,-20) Note: Do not use y=ax^2+bx+c as the equation Use: (x-h)^2=-4a(      Log On


   



Question 1187756: Find the equation of parabola with the given condition:
Axis vertical and passing through (0,0)(1,0) and (5,-20)
Note: Do not use y=ax^2+bx+c as the equation
Use: (x-h)^2=-4a(y-k)
Can you also show me the solution? Ty

Found 2 solutions by Edwin McCravy, josgarithmetic:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!




h%5E2%22%22=%22%22%281-h%29%5E2  <--since both equal 4ak

h%5E2%22%22=%22%221-2h%2Bh%5E2 <--subtract h2 from both sides

0%22%22=%22%221-2h

2h%22%22=%22%221

h%22%22=%22%221%2F2   

h%5E2%22%22=%22%221%2F4

4ak%22%22=%22%221%2F4  <--since h2 equals 4ak

%285-h%29%5E2%22%22=%22%2280a%2B4ak

%285-1%2F2%29%5E2%22%22=%22%2280a%2B1%2F4

%284%261%2F2%29%5E2%22%22=%22%2280a%2B1%2F4

%289%2F2%29%5E2%22%22=%22%2280a%2B1%2F4  

81%2F4%22%22=%22%2280a%2B1%2F4  <--multiply through by 4

81%22%22=%22%22320a%2B1

80%22%22=%22%22320a

80%2F320%22%22=%22%22a

1%2F4%22%22=%22%22a

4ak%22%22=%22%221%2F4

4%281%2F4%29k%22%22=%22%221%2F4

k%22%22=%22%221%2F4

So the equation of the parabola is

%28x-h%29%5E2%22%22=%22%22-4a%28y-k%29

%28x-1%2F2%29%5E2%22%22=%22%22-4%281%2F4%29%28y-1%2F4%29%29

You simply further.

Edwin

Answer by josgarithmetic(39620) About Me  (Show Source):