Math 2Y –

GPS AlgebraName ______________________________

You must use pencil only and be sure that you show all your work.

A. Convert from vertex form into standard form.

B. State the vertex

1. f(x) = (x + 2)2 + 12. f(x) = 2(x - 3)2 - 7

A. Convert from standard form into vertex form.

B. State the vertex

3. f(x) = x2 + 3x – 5 4. f(x) = x2 + 6x + 1

5. Sketch a graph of the function f(x) = x2 + 6x + 7

6. Describe the transformations in relation to the parent quadratic function: f(x) = 2(x- 4)2 + 9

7. Describe the transformations in relation to the parent quadratic function: f(x) = -(x + 2)2 - 1

8. In relation to the parent quadratic function, use the form:, to write a new function with a reflection in the x-axis, a horizontal shift right by 1, and a vertical shift up by 6.

9. Write a quadratic equation in STANDARD FORM that has the following transformations:

a. Horizontal shift right 5 and vertical shift down 4.

b. Vertical stretch (narrows) by 2 and a horizontal shift left 7.

Use the graphs at the right to answer the following questions.

10. What is the domain?

11. What is the range?

Use the graph at the right to answer the following questions.

12. What are the zeros?

13. What is the y-intercept?

14. What is the average rate of change over the interval ?

Calculate the average rate of change for the function on the given interval

Show all steps!

15. f(x) = 2x2 + x – 1 for 2 ≤ x ≤ 4 16. f(x) = x2 - 4x + 2 for -2 ≤ x ≤ 0

Graph the function. Identify zeros, vertex, axis of symmetry, range, and domain.

17. f(x) = x2 + 6x – 5

Vertex: ______________________________

Axis of symmetry: _____________________

Range: _______________________________

Domain: _____________________________

Interval of Increase: ____________________

Interval of Decrease: ___________________

Extrema (max or min): __________________

18. f(x) = (x + 2)2 – 8

Vertex: ______________________________

Axis of Symmetry: _____________________

Range: ______________________________

Domain: _____________________________

Interval of Increase: ____________________

Interval of Decrease: ___________________

Extrema (max or min): __________________

19. Use the graph to the above to answer the following:

a. How long was the flight of the ball?

b. What are the zeros on this graph?

c. What do the zeros represent on this graph?

d. What is the maximum height of the ball?

e. What is the domain of this graph?

f. What is the range of this graph?

g. What is the y-intercept (as an ordered pair)?

h. What does the y-intercept represent?

i. Write the equation of the graph in vertex form.

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