```Math 2
Name: _________________________
Use the quadratic equation f  x   4x2  8x  21 to complete the following tasks:
1. Does the parabola open upward or downward? ___________
How can you determine this from the equation?
2. Is the vertex a minimum or a maximum? _____________________________
How do you know?
3. What are the roots/zeros/x-intercepts of your parabola?
a. Solve by factoring and the Zero-Product Property. Show your work.
roots/zeros/x-intercepts: _______________________
roots/zeros/x-intercepts: _______________________
4. What are the coordinates of the vertex of your parabola? Show your work.
Vertex : _______________________
5. Write the equation in vertex form (by completing the square). Show your work.
Vertex : _______________________
6. What is the axis of symmetry of your parabola? ___________________________
7. What is the domain of your function? ___________________________________
8. What is the range of your function? ____________________________________
9. What is the y-intercept of your parabola? _______________________________
10. Calculate the coordinates of three other points. Show your work.
11. Carefully draw your parabola using the information you found in steps 1 – 1. Be sure to plot
AND LABEL the coordinates you have found in the previous steps to help sketch the parabola.
Pick an appropriate scale for the x- and y- axis!
Pick an appropriate scale for the x- and y- axis!
Math 2
Name: _________________________
Use the quadratic equation f  x   x2  8x  12 to complete the following tasks:
1. Does the parabola open upward or downward? ___________
How can you determine this from the equation?
2. Is the vertex a minimum or a maximum? _____________________________
How do you know?
3. What are the roots/zeros/x-intercepts of your parabola?
a. Solve by factoring and the Zero-Product Property. Show your work.
roots/zeros/x-intercepts: _______________________
roots/zeros/x-intercepts: _______________________
4. What are the coordinates of the vertex of your parabola? Show your work.
Vertex : _______________________
5. Write the equation in vertex form (by completing the square). Show your work.
Vertex : _______________________
6. What is the axis of symmetry of your parabola? ___________________________
7. What is the domain of your function? ___________________________________
8. What is the range of your function? ____________________________________
9. What is the y-intercept of your parabola? _______________________________
10. Calculate the coordinates of three other points. Show your work.
11. Carefully draw your parabola using the information you found in steps 1 – 1. Be sure to plot
AND LABEL the coordinates you have found in the previous steps to help sketch the parabola.
Pick an appropriate scale for the x- and y- axis!
Pick an appropriate scale for the x- and y- axis!
```