Answer. Third option y=4x^2
Solution:
When you multiply a function by a value with absolute value less than 1 you get a wider graph. If you multiply the function by a value with absolute value greater than 1 you get a narrower graph.
In this case we have the quadratic function y=x^2 (parent function)
1. In the first option y=-x^2 we are multiplying the parent function by -1, with absolute value 1, then the width of the graph is the same of the parent function, the minus sign only reflex the graph with respect the x-axis.
2. In the second option y=1/4x^2 we are multiplying the parent function by 1/4, with absolute value 1/4=0.25<1, then we must get a wider graph than the parent function and than the first option.
3. In the third option y=4x^2 we are multiplying the parent function by 4, with absolute value 4>1, then we must get a narrower graph than the parent function and than the first and second option.
4. In the fourth option y=1/9x^2 we are multiplying the parent function by 1/9, with absolute value 1/9=0.11<1/4=0.25<1, then we must get a wider graph than the parent function and than the second option. Of course that this graph is wider than the third oprtion.
Answer: The quadratic function y=4x^2 has the narrowest graph.