Question

Which best describes the end behavior of y=7x^2?

As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) decreases.

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) decreases.

As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.

As x > 0 increases, f(x) decreases. As x < 0 decreases, f(x) increases.

Answer 1

Call some large positive number, a>0. As larger positive values of x are used in the function,
y(x) = 7 x^2 y(a) = 7 (a)^2 <-- just a larger positive number.
As larger negative values of x are used in the function,
y(-a) = 7 (-a)^2 = 7a^2 <-- also a larger positive number. So, in both directions the values are getting larger around (0, 0).

Answer 2

So it would be: As x > 0 increases, f(x) increases. As x < 0 decreases, f(x) increases.
since in both cases it would increase.