The parabola with the equation y=4x\dfrac{1}{2}x^2 has how many points with (x,y) coordinates that are both positive integers?

×
3

×
4

×
7

×
8

×
Infinitely many
The parabola with the equation y=4x\dfrac{1}{2}x^2 has how many points with (x,y) coordinates that are both positive integers?
3
4
7
8
Infinitely many
If y>0, 4x\dfrac{1}{2}x^2>0
x(8x)>0
x(x8)<0
\therefore 0 < x<8
\because y = 4x\dfrac{1}{2}x^2
In order for y to be integers, x must be even numbers.
So x could be 2, 4, 6
A is the choice.