find t he vertex

22
Find the Vertex Transformati ons Of Functions Even Odd or Neither More Parabolas 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 10 20 30 40 50 Hardtke Jeopardy Template Click here for game DIREC TIONS

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Find t he Vertex. Transformations Of Functions. Even Odd or Neither. More Parabolas. 10. 10. 10. 10. 20. 20. 20. 20. 30. 30. 30. 30. 40. 40. 40. 40. 50. 50. 50. 50. Click here for game DIRECTIONS. Hardtke Jeopardy Template 2011. 10 Find the Vertex. - PowerPoint PPT Presentation

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Page 1: Find t he  Vertex

Findthe

Vertex

TransformationsOf

Functions

EvenOdd orNeither

MoreParabolas

1020304050

1020304050

1020304050

1020304050

Hardtke Jeopardy Template 2011Click here for game DIRECTIONS

Page 2: Find t he  Vertex

f(x) = 2(x – 1)2 – 3Click to check answer

(1, -3)Inside the function move in same directionOutside the function move in opp direction

Click to return to game board

10 Find the Vertex

Page 3: Find t he  Vertex

f(x) = 2x2 – 12x + 1Click to check answer

(3, -17)Use –b/2a to find the x-coord and then plug

that into f(x) to find the y-coord.Click to return to game board

20 Find the Vertex

Page 4: Find t he  Vertex

y = 6 – 2x2

Click to check answer

(0, 6)y = -2x2 + 0x + 6 -b/2a = 0/-4 = 0Plug 0 in for x to get y-coord of 6

Click to return to game board

30 Find the Vertex

Page 5: Find t he  Vertex

x = -2(y - 4)2 + 5Click to check answer

(5, 4)Inside the function move in same direction for yOutside the function move in opp direction for x

Click to return to game board

40 Find the vertex

Page 6: Find t he  Vertex

x = -2y2 - 8y - 1Click to check answer

(7, -2)-b/2a to find the y-coord

Plug that value into y to find the x-coord.

Click to return to game board

50 Find the Vertex

Page 7: Find t he  Vertex

Compared to f(x) = | x|, g(x) = | x – 7| is shifted 7 units in

this direction. Click to check answer

RightShifts inside a function move in the

opposite directionClick to return to game board

10 Transformations

Page 8: Find t he  Vertex

g(x) if it is f(x) = flipped vertically.

Click to check answer

Vert flip opposite outside the function

Click to return to game board

20 Transformations

Page 9: Find t he  Vertex

g(x) if it is f(x) = shifted down 2 units

and left 3 units. Click to check answer

Horiz shift inside the function in opp direction Vert shift outside the function in same direction

Click to return to game board

30 Transformations

Page 10: Find t he  Vertex

f(x) = ln x and g(x) = -3 ln x, then g(e) = ?

Click to check answer

– 3Every y-coordinate is flipped vertically and stretched

by a multiple of 3Click to return to game board

40 Transformations

Page 11: Find t he  Vertex

Given that (2, 8) is on f(x) = x3, give a transformation of function f that

passes through (3, -24).

Click to check answer

f(x) = – 3(x – 1)3 May be other answers, but easy to shift right

1, flip vertically & stretch by multiple of 3

Click to return to game board

50 Transformations

Page 12: Find t he  Vertex

f(x) = – 3 | x |Click to check answer

EvenGraph has symmetry to y-axis

Notice that f(-4) = f(4).

Click to return to game board

10 Even, Odd or Neither

Page 13: Find t he  Vertex

Click to check answer

EVENParabola open down with vertex on the y-axis so

it has y-axis symmetry. E.G., notice that f(-2) = f(2) = -11

Click to return to game board

20 Even, Odd or Neither

Page 14: Find t he  Vertex

x = - y2Click to check answer

NeitherParabola open to the left. It has symmetry to the x-

axis, but it is not a function (fails vert line test) and it is neither even nor odd

Click to return to game board

30 Even, Odd or Neither

Page 15: Find t he  Vertex

f(x) = – 3x3 + xClick to check answer

ODDSymmetry to the origin. E.G. notice that (1, -

2) and (-1, 2) are on f(x). That is f(-x) produced – f(x).

Click to return to game board

40 Even, Odd or Neither

Page 16: Find t he  Vertex

f(x) = sin xClick to check answer

ODDSymmetry to origin. E.G. and are on the

graph. That is f(-x) produced – f(x).

Click to return to game board

50 Even, Odd or Neither

Page 17: Find t he  Vertex

If a parabola has its vertex at (1,3) and opens to the right and (2, 7) is on the parabol, what other point do you know is on the parabola?

Click to check answer

(2, -1)7 is 4 above the axis of y = 3, so we need to also go 4

units below the axisClick to return to game board

10 More Parabolas

Page 18: Find t he  Vertex

Give the equation of a parabola with vertex on the y-axis that has the x-

axis as its axis of symmetry.Click to check answer

x = y2 or x = -y2Sideways so opens to the left or right.

Click to return to game board

20 More Parabolas

Page 19: Find t he  Vertex

Give the equation of a parabola that opens left with vertex

(-3, 1) Click to check answer

x = -a(y – 1)2 - 3Any value of a as long as it is a negative number

Click to return to game board

30 More Parabolas

Page 20: Find t he  Vertex

Give the equation of a parabola that opens down with vertex

(-7, -5)Click to check answer

y = -a(x + 7)2 - 5Any value of a as long as it is negative.

Click to return to game board

40 More Parabolas

Page 21: Find t he  Vertex

Find the vertex or graphing form of 4y + x = 2y2 - 1

Click to check answer

x = 2(y – 1)2 - 3Step 1: x = 2y2 – 4y - 1

Step 2: x = 2(y2 – 2y _____) – 1_______Step 3: x = 2(y2 – 2y +1) – 1 - 2

Click to return to game board

50 More Parabolas

Page 22: Find t he  Vertex

Jeopardy Directions• Any group member may select the first question and students rotate choosing the next

question in clockwise order regardless of points scored.

• As a question is exposed, EACH student in the group MUST write his solution on paper. (No verbal responses accepted.)

• The first student to finish sets down his pencil and announces 15 seconds for all others to finish working.

• After the 15 seconds has elapsed, click to check the answer.– IF the first student to finish has the correct answer, he earns the point value of the question and no

other students earn points.– IF that student has the wrong answer, he subtracts the point value from his score and EACH of the

other students with the correct answer earns/steals the point value of the question. (Those students do NOT lose points if incorrect, only the first student to “ring in” can lose points in this game version.)

• Each student should record a running total of his own score.

• Good sportsmanship and friendly assistance in explaining solutions is expected! Reviewing your math concepts is more important than winning.

Return to main game board