Question

Which of the quadratic functions has the narrowest graph? (1 point) y = –x^2 y = 1/4x^2 y = 4x^2 y = 1/9x^2

Answer 1

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.

   

Answer 2

Y = 1/4² has the narrowest graph. 

When 0 < |a| < 1, the graph is wider.
When |a| > 1, the graph is narrower. 

For the equation y = -x², a = -1.
0 < |-1| < 1 
0 < 1 < 1

This statement is not true, so the parabola is narrower.


For the equation y = 4x², a = 4.

0 < |4| < 1
0 < 4 < 1 

This statement is false, so the parabola is narrower also.

For the equation y = 1/4x², a = 1/4. 

0 < |1/4| < 1
0 < 1/4 < 1

This statement is true, so the parabola is wider.

For the equation y = 1/9x², a = 1/9

0 < |1/9| < 1
0 < 1/9 < 1 

This statement is true, so the parabola is wider.

Now you can eliminate the 2 wider parabolas because you are looking for the quadratic function that has the narrowest graph. 


     When you choose between the two narrow parabolas, you have to look at the value for a in each equation. The closer the "a value" is to zero, the wider the parabola will be. The further away the "a value" is to zero, the narrower a parabola will be. In your case, the equation y = 4x² is narrower than y = -x² because it's a value is higher, making the parabola skinnier. 

I hope this helps you!