Place a rimmed sheet pan in the oven and preheat to 450 degrees F.
Add the olive oil, garlic powder, onion powder, smoked paprika, a generous pinch each of salt and pepper to a large bowl and whisk to combine. Add all the prepped veggies and toss to completely coat in the olive oil-spice mixture.
Carefully remove the hot sheet pan from the oven. Transfer the vegetables to the hot pan and spread them out into an even layer. Roast, stirring the vegetables halfway, until the potatoes are fork tender and golden, 25 to 30 minutes.