Given the graph below write the function for fx in standard

Given the graph below, write the function for f(x) in standard form.

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Now since the parabola indicated in the figure is opening upwards, the parabola is of the form

(x-a)^2 = M(y-b)

Clearly vertex of the parabola is 4,-4 ,Hence a = 4 and b = -4

(x-4)^2 = M (y+ 4)

x^2 -8x + 16 = M (y + 4)

Clearly the curve passes through the polint 2,0

Hence 2,0 should satisfy the above curve

2^2 - 8*2 + 16 = M (4)

=> M = 1

Hence the equation of the curve shall be

(x-4)^2 = (y + 4)

x^2 -8x = y - 12

Solution