Unit 2: Parent Graphs

Name:______

Unit 2: Parent Graphs

2.1 Graphing Quadratics in Vertex Form

2.2 Transforming Parent Functions

2.3 Transforming Non-Functions

2.4 Piecewise Functions

Algebra 2Name:______Bk:______

2.1 Notes, Graphing Quadratics in Vertex Form

Graph the following quadratic equations on the given set of axes. Label the vertex for each parabola.

1. 2. 3. 4.

5. 6. 7. 8.

Graph the following quadratic equations on the given set of axes. Label the vertex for each parabola.

9. 10. 11. 12.

13. 14. 15.

16.

Write a new equation to shift the parabola according to the conditions in each problem. Then, write the vertex of your new parabola.

17. Find a way to change the equation to make the y = x² parabola vertically compressed (wider), open down, move six units up, and move two units to the left.

18. Find a way to change the equation to make the y = x² parabola vertically stretch (narrower), move three units down, and move five units to the right.

19. Find a way to change the equation to make the y = x² parabola open down, vertically compressed (wider), and move two units down.

20. Find a way to change the equation to make the y = x² parabola open down, move up four units, and move five units to the left.

Vertex form for a Quadratic Function:

Vertex: (h, k)

The value of a can cause the graph to flip (open down) and can cause it to be stretched (narrower) or compressed (wider).

Graph the following quadratic equations on the given set of axes. Label the vertex for each parabola.

21.22.

23.24.

Algebra 2Name:______Bk:______

2.1 Homework, Graphing Quadratics in Vertex Form

Graph the following quadratic equations on the given set of axes. Label the vertex for each parabola, then state the domain and range.

1. 2.

D:D:

R:R:

3. 4.

D:D:

R:R:

Write a new equation to shift the parabola according to the conditions in each problem. Then, write the vertex of your new parabola.

5. Find a way to change the equation to make the y = x² parabola vertically compressed (wider), open down, move five units up, and move three units to the left.

6. Find a way to change the equation to make the y = x² parabola vertically stretch (narrower), move four units down, and move six units to the right.

7. Find a way to change the equation to make the y = x² parabola vertically compressed (wider), and move two units down.

8. Find a way to change the equation to make the y = x² parabola vertically stretch (narrower), open down, move up ten units, and move eight units to the left.

Algebra 2Name:______Bk:_____

2.2 Notes: Transforming other parent functions

Square Root Functions:

1. 2. 3.

4.5. 6.

7.Given the following function (without graphing), explain what will happen to the parent function:

8.Given the following function (without graphing), explain what will happen to the parent function:

9.Given the following function (without graphing), explain what will happen to the parent function:

Absolute Value Functions:

10. 11. 12.

13.14. 15.

16.Given the following function (without graphing), explain what will happen to the parent function:

17.Given the following function (without graphing), explain what will happen to the parent function:

18.Given the following function (without graphing), explain what will happen to the parent function:

Cubic Functions:

19. 20. 21.

22.23. 24.

25.Given the following function (without graphing), explain what will happen to the parent function:

26.Given the following function (without graphing), explain what will happen to the parent function:

27.Given the following function (without graphing), explain what will happen to the parent function:

Cube Root Functions:

28. 29. 30.

31.32. 33.

34.Given the following function (without graphing), explain what will happen to the parent function:

35.Given the following function (without graphing), explain what will happen to the parent function:

36.Given the following function (without graphing), explain what will happen to the parent function:

Rational (Hyperbola) Functions:

37. 38. 39.

40.41. 42.

43.Given the following function (without graphing), explain what will happen to the parent function:

44.Given the following function (without graphing), explain what will happen to the parent function:

45.Given the following function (without graphing), explain what will happen to the parent function:

Exponential Functions:

46. 47. 48.

49.50. 51.

52.Given the following function (without graphing), explain what will happen to the parent function:

53.Given the following function (without graphing), explain what will happen to the parent function:

54.Given the following function (without graphing), explain what will happen to the parent function:

55. How can you tell if a graph will be vertically stretched?

56. How can you tell if a graph will be vertically compressed?

57. What does the h value represent?

58. What does the k value represent?

59. State the domain and range for the following graphs:

#6D:R:

#15D:R:

#24D:R:

#33 D:R:

#42 D:R:

#51 D:R:

Parent Function / Family / General Equation / What is the relevance of (h, k)?
/ Absolute Value /
/ Quadratic (Parabola) /
/ Cubic /
/ Rational (Hyperbola) /
/ Square root /
/ Exponential /
/ Cube Root /

Algebra 2Name:______Hr:______

2.2 Homework: Transform Parent Functions

Match each function with its equation and graph.

1. Quadratic: EquationsGraphs

Equation _____ A.H.

Graph _____

2. Absolute Value:

Equation _____ B.I.

Graph _____

3. Cubic:

Equation _____ C.J.

Graph _____

4.Rational:

Equation _____D.K.

Graph _____

5. Cube Root:

Equation _____ E.L.

Graph _____

6. Exponential:

Equation _____ F.M.

Graph _____

7. Square Root:

Equation _____ G.N.

Graph _____

Sketch the graph for each of the following functions.

8.9.

10.11.

12.13.14.

Algebra 2Name:______Bk:_____

2.3 Notes: Transforming Non-Functions

Begin by fully investigating x = y2and x2 + y2 = 25.

Without using a graphing calculator, make a table and a graph for each equation.

x = y2 x2 + y2 = 25

x / y
x / y

In the equation x = y2, look at your table for an x-value of 4, you found a y-value of 2. WAIT! Is there another possible value for y? Decide if there are more points you could add.

Describe x = y2and x2 + y2 = 25completely by stating the domain and range of each equation, finding the important points such as intercepts, and what happens to y as x increases.

How are these two relationships different form others you have been working with?

Rewrite x = y2and x2 + y2 = 25so that you can graph them in a graphing calculator. (hint: get to y =)

Graph both with your graphing calculator. Do they look like the graphs you made above?

Math Notes:

Circle: set of all points in a plane that are equidistant from a given point in the plane called the center

Radius: any segment whose endpoint are the center and a point on the circle

Assume:

(x , y) – coordinates of a point on the circle

(h, k) – coordinates of the center of the circle

r – length of the radius

A circle has a special characteristic, its radius, which defines its size.

What is the radius of x2 + y2 = 25?

How is the radius of the circle related to the equation?

What would the equation of a circle be that has its center at (5, -7) with radius 10?

10. What would the equation of a circle be that has its center at (5, -7) with radius 20?

Generalize the connection between the radius and the equation of a circle. What is the general equation for a circle with any center (h, k) and radius r.

Given the equation, what is the radius of the circle and what is the center of the circle?

Write a new equation of a circle by moving it right three, and down five with a radius of 6.

Then:

Equations of a circle can be found using the distance formula

Distance Formula:

h is the horizontal shift

k is the vertical shift

r is the length of the radius

Algebra 2Name:______Bk:_____

2.3 Homework: Transforming Non-Functions

Identify the center and radius of each. Then sketch the graph.

Center: Center:

Radius: Radius:

3. 4.

Center: Center:

Radius: Radius:

Write a new equation to shift the circle according to the conditions in each problem. Then, write the center of your new circle.

5. Find a way to change the equation to make the x2 + y2 = r2 move five units up, and move three units to the left with a radius of 10.

6. Find a way to change the equation to make the x2 + y2 = r2 move four units down, andmove one unit to the left with a radius of 3.

7. Find a way to change the equation to make the x2 + y2 = r2 move four units to the left witha radius of 4.

8. Find a way to change the equation to make the x2 + y2 = r2 move six units to the right, and move 5 units up with a radius of 4.

Algebra 2Name:______Bk:_____

2.4 Notes, Piecewise Functions

Domain:______Domain:______

Range:______Range:______

3. 4.

Domain:______Domain:______

Range:______Range:______

5. 6.

Domain:______Domain:______

Range:______Range:______

7.8.

Domain:______Domain:______

Range:______Range:______

9. 10.

Domain:______Domain:______

Range:______Range:______

11.12.

Domain:______Domain:______

Range:______Range:______

Step Function

13.Labor costs at the Fix-It Auto Repair Shop are $60 per hour or any fraction thereof. Draw a graph that represents this situation.

14.A downtown parking lot charges $2 for the first hour and $1 for each additional hour

or part of an hour. Draw a graph that represents this situation.

15.One psychologist charges for counseling sessions at the rate of $65 per hour or any fraction thereof. Draw a graph that represents this situation.

Algebra 2Name:______Bk:____

2.4 Homework, Piecewise Functions

Graph the following piecewise functions. State the domain and range for each.

Domain: ______

Range: ______

Domain: ______

Range: ______

Domain: ______

Range: ______

Domain: ______

Range: ______

Domain: ______

Range: ______

Domain: ______

Range: ______

Algebra 2 Name:______Bk:_____

2.4 Extra Practice: Piecewise Functions

Write the piecewise function for each. Make sure to define the x-values for each piece of the graph.