For the equation y = 3x², what happens to the value of y when x is doubled?

We are testing the effect of doubling x on the equation y = 3x². Let's pick a starting value for x, for example, x = 10. The original y would be y = 3 * (10)² = 3 * 100 = 300. Now, let's double x. The new x is 2 * 10 = 20. The new y will be y = 3 * (20)² = 3 * 400 = 1200. Comparing the new y (1200) to the original y (300), we see that 1200 = 4 * 300. The value of y has been multiplied by 4. Algebraically: Original: y = 3x² New x: x_new = 2x New y: y_new = 3(x_new)² = 3(2x)² = 3(4x²) = 12x². Since the original y was 3x², the new y (12x²) is 4 * (3x²), which is 4 times the original y.