Question 473484
Find the equation of quadratic function that has the given vertex and given point. 
Vertex (1,3) passing through (4,8)
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What we have here is a parabola of standard form: y=A(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex. A is a multiplier which affects the steepness of the curve.
For given problem:
y=A(x-1)^2+3
Using (x,y) coordinates of given point (4,8) to solve for A
8=A(4-1)^2+3
8-3=A(3)^2
5=9A
A=5/9
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Equation:
y=(5/9)(x-1)^2+3
see graph below as a visual check on answer:

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{{{ graph( 300, 300, -10, 10, -10, 10, (5/9)(x-1)^2+3) }}}