Final answer:
The function f(x) = 5x² + 45 has no x-intercepts because setting f(x) to 0 yields no solutions, the output will always be positive.
Step-by-step explanation:
The x-intercepts of a parabola given by the function f(x) = 5x² + 45 can be found by setting the output of the function, f(x), equal to zero and solving for the variable x. However, notice that in this function, there is no x-term that does not involve a square and the constant term is positive. This means that no matter what value of x we plug into the function, the output will always be positive due to the square and added positive 45. Therefore, the equation f(x) = 0 has no solution and the parabola has no x-intercepts.