Answer:
The y values for the given x-values differ from those in the function y = x^2. In this case, the values are twice as large as those in the function y = x^2 for the same x-values. The graph of y = 2x^2 is narrower and steeper, with larger y-values for the same x-values compared to the chart of y = x^2.
Explanation:
The equation y = 2x^2 represents a quadratic function, and it is different from the function y = x^2 in that it has a coefficient of 2 in front of the x^2 term. This coefficient affects the shape of the graph, making it narrower and steeper than the graph of y = x^2.
Let's calculate some values to see how the graphs of these two functions differ:
For y = 2x^2:
When x = -3, y = 2(-3)^2 = 2(9) = 18
When x = -2, y = 2(-2)^2 = 2(4) = 8
When x = -1, y = 2(-1)^2 = 2(1) = 2
When x = 0, y = 2(0)^2 = 2(0) = 0
When x = 1, y = 2(1)^2 = 2(1) = 2
When x = 2, y = 2(2)^2 = 2(4) = 8
When x = 3, y = 2(3)^2 = 2(9) = 18
So, the values of y for the given x-values are different from those in the function y = x^2. In this case, the values are twice as large as those in the function y = x^2 for the same x-values. The graph of y = 2x^2 is narrower and steeper, with larger y-values for the same x-values compared to the chart of y = x^2.