Plotting of functions:
• y = 3x²,
,
• y = x²,
we get the following curves:
1) Graph of y = 3x²
From the graph, we see that we have a parabola that:
• opens up,
,
• has the y-axis as the axis of symmetry,
,
• has the origin as its vertex.
2) Comparison
Comparing the graphs of y = 3x² and y = x², we see that both curves:
• opens up,
,
• has the y-axis as the axis of symmetry,
,
• has the origin as its vertex.
The difference between the curves is that y = 3x² grows up more rapidly than y = x², this is due to the multiplicative constant in front of x². For the same value of x, the function y = 3x² will be 3 times greater than the function y = x².