Final answer:
To identify the parabola with a range of y <= 5 that passes through 0,2, we can use the general equation of a parabola: y = ax + bx^2. By substituting the coordinates (0,2) and solving for the coefficients, we find that the equation of the parabola is y = 2x.
Step-by-step explanation:
To identify the parabola with a range of y <= 5 that passes through the point (0,2), we can use the general equation of a parabola: y = ax + bx². Since the range is y <= 5, we know that a + b <= 5. Substituting the coordinates (0,2) into the equation, we get 2 = a(0) + b(0²). From this, we find that a = 2 and b = 0.
Therefore, the equation of the parabola that satisfies the given conditions is y = 2x.