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Comparing Graphs

How do the graphs of $y=x^2$ and $y=3x^2$ compare?

Plot both graphs.

$y=x^2$

x = 1 → (1, 1)

x = 2 → (2, 4)

x = -2→ (-2, 4)

x = -1 → (-1, 1)

x = 3 → (3, 9)

x = -3 → (-3, 9)

x = 4 → (4, 16)

x = -4 → (-4, 16)

x = 0 → (0, 0)

$y=3x^2$

x = 0 → (0, 0)

x = 1 → (1, 3)

x = 2 → (2, 12)

x = 3 → (3, 27)

x = 4 → (4, 48)

x = -1 → (-1, 3)

x = -2 → (-2, 12)

x = -3 → (-3, 27)

x = -4 → (-4, 48)

The $y=3x^2$ plot grows faster. This is because of the 3 coefficient. $y=3x^2$ is narrower which is a sign of fast growth.