Question

Calculate the number of points with $(x,y)$ coordinates that are both positive integers in the parabola with the equation $y=4x-\frac{1}{2}{x}^2$.

• A. $3$
• B. $4$
• C. $7$
• D. $8$
• E. Infinitely many

Answer 1

The correct option is C $7$

• given that both $x$ and $y$ should be positive
• we get $4x-\frac{x^2}{2}>0$ which implies $x$ belongs to $(0,8)$
• Therefore the number of positive integers of $x$ such that $y$ should be positive is $7$