In each exercise, you are presented with 2 quadratic functions.

### Instructions

1. Determine the differences between the graphs.

Differences to choose from:

A. Graph shifts up

B. Graph shifts down

C. Graph opens wider

D. Graph opens more narrow

E. Graph rotates 180 degrees

Each exercise has either one, two, or no differences.

2. Answer the questions *without *using a graph.

### Answers

1. How is *y* = 3/2*x*^{2} + 7 different from *y* = -3/2*x*^{2 }?

The graph of *y* = 3/2*x*^{2} + 7 **shifts up 7 units** and **rotates 180 degrees**.

2. How is *y* = *x*^{2} - 5 different from *y* = 5*x*^{2} + 3?

The graph of *y* = *x*^{2} - 5 **shifts down 8 units** and **opens wider**.

3. How is *y* = 4*x*^{2} - 9 different from *y* = 2*x*^{2} - 6?

The graph of *y* = 4*x*^{2} - 9 **shifts down 3 units** and **opens more narrow**.

4. How is *y* = -8*x*^{2 }different from *y* = -*x*^{2} - 8?

The graph of *y* = -8*x*^{2 }**shifts up 8 units** and **opens more narrow**.

5. How is *y* = -4 + 2*x*^{2} different from *y* = 2*x*^{2} - 4?**No difference**

6. How is *y* = 3/2*x*^{2 }+ 7 different from *y* = 5*x*^{2 }+ 3?

The graph of *y* = 3/2*x*^{2 }+ 7 **shifts up 4 units** and **opens wider**.

7. How is *y* = -4*x*^{2 }+ 4 different from *y* = -2*x*^{2}?

The graph of *y* = -4*x*^{2 }+ 4 **opens more narrow** and **shifts up 4 units**.

8. How is *y* = 1/2*x*^{2 }different from *y* = -1/2*x*^{2} - 8?

The graph of *y* = 1/2x^{2 }**shifts up 8 units** and **rotates 180 degrees**.

9. How is *y* = 5*x*^{2} + 1 different from *y* = 1.25*x*^{2}?

The graph of *y* = 5*x*^{2} + 1 **shifts up 1 unit** and **opens more narrow**.

10. How is *y* = 2*x*^{2} - 3 different from* y* = 3*x*^{2 }+ 2?

The graph of *y* = 2*x*^{2} - 3 **shifts down 5 units** and **opens wider**.