Preheat your oven to 350°F (175°C).
In a mixing bowl, combine the flour, baking soda, and salt.
In another bowl, whisk together the yogurt, sugar, eggs, vanilla extract, and vegetable oil.
Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
Pour the batter into a greased loaf pan.
Bake for 45 minutes, or until a toothpick inserted into the center comes out clean.
Let the bread cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.