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(y-k)=a(x-h)^2

given (h, k ) = (1,1)

put the values

(y-1)=a(x-1)^2

now put the values from other point (0,3)

(3-1)=a(0-1)^2

2 = a

put the value of a in parabola equation

(y-1)=2(x-1)^2

for x intercept y=0

so

(0-1)=2(x-1)^2

-1 = 2 (x^2 +1 -2x)

-1/2 = (x^2 +1 -2x)

x^2 +1 -2x +1/2 = 0

x^2-2x+1.5 = 0

solve it by using quadratic formula

you will get values of x which are x = 1+0.707i and 1-0.707i

so the answer for x intercept are

(x2,y2) = (1+0.707i , 0)

(x2,y2) = (1- 0.707i , 0)

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