Preheat oven to 350 degrees F (175 degrees C). Grease and flour one 9x13 inch pan.
In a medium bowl, sift together the flour, baking soda, baking powder and salt. In a separate bowl, cream together the butter and sugar. Beat in the eggs one at a time, then stir in the vanilla. Beat in the mashed bananas. Gradually stir the sifted ingredients into the banana mixture. Spread evenly into the prepared pan.
Bake for 30 to 40 minutes in the preheated oven, or until a toothpick inserted into the center of the cake comes out clean. Let cool in the pan for 10 minutes, then turn out onto a wire rack and cool completely.
Interesting Facts
Bananas are one of the most popular fruits in the United States.
Bananas are a good source of potassium and fiber.
Banana cake is a popular dessert in many countries.