Question 1176688
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Recall that 
{{{y = a(x-h)^2 + k}}}
represents the generalized vertex form. 
a = leading coefficient
h = x coordinate of vertex
k = y coordinate of vertex


Since the vertex given to us is (1,3), this means (h,k) = (1,3)
In other words,
h = 1
k = 3


We're also told the parabola passes through (x,y) = (2,6)
x = 2
y = 6



We have these four items of info
h = 1
k = 3
x = 2
y = 6


Plug those four items into the first equation mentioned and isolate 'a'.
{{{y = a(x-h)^2 + k}}}


{{{6 = a(2-1)^2 + 3}}}


{{{6 = a(1)^2 + 3}}}


{{{6 = a + 3}}}


{{{6-3 = a}}}


{{{3 = a}}}


{{{a = 3}}}
The leading coefficient is positive, so the parabola opens upward.


We have
{{{y = a(x-h)^2 + k}}}
turn into
{{{y = 3(x-1)^2 + 3}}}
after plugging in a = 3, h = 1, k = 3


We could expand things out and combine like terms like so
{{{y = 3(x-1)^2 + 3}}}


{{{y = 3(x^2-2x+1) + 3}}} FOIL rule


{{{y = 3x^2-6x+3 + 3}}} Distribute


{{{y = 3x^2-6x+9}}} Combine like terms


The vertex form {{{y = 3(x-1)^2 + 3}}} expands and simplifies to the standard form {{{y = 3x^2-6x+9}}}


Graph:
<img src = "https://i.imgur.com/VmRF2eN.png">
note the vertex is the lowest point at (1,3)
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