To find the constant term in the function f(x) = x² + 8x, we begin by considering the fact that the x-intercepts of a function are the values of x where the function equals zero.
Given the x-intercepts at 3 and 5, we can express the function in factored form:
f(x) = (x – 3)(x – 5)
Now, let’s expand this product:
f(x) = x² – 5x – 3x + 15 = x² – 8x + 15
From this expansion, we can see that the constant term is 15. Therefore, the complete quadratic function can also be compared with the standard form f(x) = x² + 8x, but in this case, we need to set our function correctly to match the given x-intercepts.
Thus, the correct constant term in the function is 15.