Question 171023
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 = {{{6/56}}}
a = {{{3/28}}}
:
Find k using 25a + k = 0
25*({{{3/28}}}) + k = 0
{{{75/28}}} + k = 0
k = {{{-75/28}}}
:
The equation:
y = {{{3/28}}}(x - 9)^2 - {{{75/28}}}
:
Plots this:
{{{ graph( 300, 200, -5, 20, -4, 10, (3/28)(x-9)^2 - (75/28)) }}}
:
Looks about right