Question 50 Answer and Explanation _ACT OG3 Form 3MC Math Section

50. The 3 parabolas graphed in the standard (x, y) coordinate plane below are from a family of parabolas. A general equation that defines this family of parabolas contains the variable n in addition to x and y. For one of the parabolas shown, n = 1; for another, n = 2; and for the third, n = 3. Which of the following could be a general equation that defines this family of parabolas for all n ≥ 1 ?

F. $y=n{x}^{2}+1$

G. $y=\frac{1}{n}{x}^{2}+1$

H. $y={x}^{2}+n$

J. $y=-n{x}^{2}+1$

K. $y=-\frac{1}{n}{x}^{2}+1$

Answer and Explanation

Your Answer is

Correct Answer is F

Explanation

Because all curves pass through the point (0, 1), H is excluded. And because the function image changes as the n value increases, GJK is excluded. Therefore, F is selected.