Station 1: Translations. 1. Translate the figure below J K L

Transcription

1 Station 1: Translations 1. Translate the figure below J K L

2 Station 2: Rotations *Assume counterclowise; clockwise is opposite 1. Rotate the figure 90 degrees according to the directions. List the coordinates of the image. P Q R Name the image of the point (-2, 3) rotated 270 degrees counterclockwise about the origin.

3 Station 3: Reflections

4 Station 4: Mixed Transformations

5 1. Solve for x in the figure below Station 5: Midsegment 2. Solve for x and y in the triangle if the segment in the middle is a midsegment. 3. Solve for x if BC is a midsegment.

6 Station 6: Congruent Triangles Determine if the triangles are congruent. If yes, make a congruency statement and give the reason why they are congruent. If they are not congruent, write not congruent. 1. ΔABC Δ by 2. ΔABC Δ by 3. ΔABC Δ by 4. What additional information do you need to prove that triangle QRS is congurent to triangle QTS by AAS?

7 Station 7: Triangles 1. Solve for x 2. Solve for x 3. Solve for x in the isosceles triangle. 4. Solve for x in the isosceles triangle

8 Station 8: Similar Figures 1. Solve for x and y in the following similar figures. 2. Solve for x and y in the following similar figures and then find the perimeter of each triangle A tree 24 feet tall casts a shadow 12 feet long. Brad is 6 feet tall. How long is Brad's shadow? (draw a diagram and solve) 5. Solve the proportion

9 Station 9: Fred Functions 1. List the transformations needed to graph the following. Remember that translations are done last. a. y = b. y = c. y = d. y = 3F(-x) e. y = 5F(x+1) Use Harry to answer the following questions a. What is the domain of Harry? b. What is the range of Harry? c. Is Harry a function? Explain. 3. Consider a new function, Julie, J(x). Julie s Domain is. Its range is. Use your understanding of transformations of functions to determine the domain and range of each of the following functions. (Hint: You may want to write the effect to Polly first.) a. J(x) 2 b. J(x + 2) Domain: Domain: Range: Range:

10 Remember: Standard Form Axis of Symmetry Station10: Graphing Quadratics in Standard Form Vertex: Plug in x from the A.O.S Solutions Factor or use quadratic formula Y-Intercept When x=0, solve for y If a is negative, opens down and maximum, if a is positive, opens up and minimum #1 y= -2x 2 + 8x 5 Axis of Symmetry Y-Intercept Vertex and Min or Max? Solutions (Zeros) Graph #2 y= -x 2 + 4

11 Station 11: Graphing and Transforming Quadratics Vertex Form Remember: Vertex Form Vertex (h, k) *remember h changes signs! Transformations -(x) reflect over the x-axis a(x) if a is greater than 1 then vertical stretch, if a is smaller than one then vertical shrink (x+ ) move left, (x- ) move right (x) + move up, (x) - move down If a is negative, opens down and maximum, if a is positive, opens up and minimum #1 y= -2(x-1) 2 +3 Transformation (in words) Y-Intercept (when x=0) Vertex Graph #2 y= (x+2) 2 1 #3 y=-(x+3) 2 2

12 Station 12: Mixed Factoring and Simplifying Polynomials GCF: Write all of the factors and identify what each term has in common. This will be your GCF. If you have 4 terms then you must divide it into two parts and then find the GCF of each part. 1. 4x 5 + 8x 4 36x *Hint GCF 2. 14x 2-9x+1 *Hint X-Box 3. 3x 3 2x 2 9x + 6 *Hint GCF by grouping 4. 3x 2 +10x-25 *Hint X-Box 5. Simplify the following by foil or box method (3x+1)(x 7)

13 Station 13: Quadratic and Discriminant 1. Solve the trinomial 2x 2 +9x +4 = 3 using the quadratic formula 2. Solve the trinomial 8x 2-10 = 5x using the quadratic formula. 3. Using the discriminant, identify how many solutions 2x 2 + 2x 1= 9 has. 4. Using the discriminant, identify how many solutions 9x = 0 has.

14 Station 14: Quadratic Word Problems 1. You are throwing a water balloon out of a window and the height of the water ballon, h, after t seconds is modeled by the equation h(t)= -16t 2 +64x +52. a. Find the maximum height the balloon reaches. b. When does the balloon reach the maximum height c. How high is the balloon after 0.25 seconds? d. When will the balloon hit the ground? 2. If a toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation h(t) = -16t t. a. How long will it take for the rocket to return to the ground? b. How long will it be until the rocket is at its maximum height? c. What is the maximum height?

15 Station 15: Quadratic Inequalities 1. Graph the quadratic in equality y > x 2 4. Hint: Use a table to help you graph the equation. 2. Graph y x 2 + x 6

16 Station 16: Random 1. If the coordinates of triangle P Q R are P (2, 4), Q (-3, 5) and R (1, 0), what are the coordinates of PQR if the translation from PQR to P Q R is (x+1, y-3). (Be careful, this one is tricky!) 2. What is the y-intercept of the quadratic graph of y=3(x+1) Factor the expression -16x 5 40x Given ΔABC ΔDEF, and CB= 3x+4 and EF=5x-10, solve for x.