area of square = 16 , so length of side = 4

square is centered at 0,0 so the coordinates of square should be (-2,2) (2,2) (2,-2) (-2,-2)

now f(x) = kx^{2}

it is given that k is positive and x^{2} will always be positive as it is a square

Therefore f(x) should always be positive

So f(x) can only intersect (-2,2) or (2,2) because the y coordinate is positive.

now put (-2,2) in the equation

2 = k * (-2)^{2}

k = 1/2 = 0.5

you can also try for (2,2)

2 = k * (2)^{2}

k = 0.5

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