Final answer:
To find the equation of the parabola with x intercepts at (-1.6, 0) and (-3.2, 0) and a y intercept at (0, -25.6), we use the standard form of a parabola and find that the equation is f(x) = 5(x+1.6)(x+3.2).
Step-by-step explanation:
The student is asking to write the equation of a parabola that has specific x intercepts and a y intercept. To find this parabolic equation, we use the fact that a parabola with x intercepts at (h, 0) and (k, 0) can be written as f(x) = a(x-h)(x-k), where a is a constant that can be determined using another point on the parabola, such as the y intercept.
In this case, the x intercepts are (-1.6, 0) and (-3.2, 0), which gives us the equation f(x) = a(x+1.6)(x+3.2). We also know the y intercept is (0, -25.6), which means when x = 0, f(x) = -25.6. Plugging these values into the equation, we get -25.6 = a(0+1.6)(0+3.2). Solving for a, we find that a = 5. Hence, the equation of the parabola is f(x) = 5(x+1.6)(x+3.2).