If y is directly proportional to x^2 and y=1/8 when x=1/2, what is the positive value of x when y=9/2?

Question

please expain how you got your answer

Answer 1

y is directly proportional to x^2

y=kx^2, where k is any constant

y=1/8 when x=1/2

1/8 = k (1/2)^2

1/8 =k/4

k=4/8=1/2

y = (1/2)x^2

when y=9/2

9/2 =(1/2)x^2

9=x^2

x=3

( strictly + or -3)

Answer 2

yαx^2, y=1/8 when x=1/2

solution

y=kx^2 where k is constant of proportionality

1/8=k(1/2)^2

1/8=k(1/4)

k=4/8

k=1/2

now when y=9/2

9/2=1/2(x^2)

x^2=9

x=3(positive value)

Answer 3

y = k * x^2

1/8 = k * (1/2)^2 => k = 1/2

9/2 = 1/2 * x^2 => x^2 = 9 => x=3

Answer 4

Direct proportion:  y = kx²

1/8 = k*(1/2)²

1/8 = 1/4k

1/2 = k

y = 1/2x²

9/2 = 1/2x²

9 = x²

3 = x

Is this an SAT question?

Answer 5

y = k x²

1/8 = k / 4

k = 1/2

x² = 2 y

x² = 9

x = 3