Find the Vertex Transformations Of Functions Even Odd or Neither More Parabolas Hardtke Jeopardy Template 2011 Click here for game DIRECTIONS

f(x) = 2(x – 1) 2 – 3 Click to check answer (1, -3) Inside the function  move in same direction Outside the function  move in opp direction Click to return to game board 10 Find the Vertex

f(x) = 2x 2 – 12x + 1 Click 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

y = 6 – 2x 2 Click to check answer (0, 6) y = -2x 2 + 0x + 6  -b/2a = 0/-4 = 0 Plug 0 in for x to get y-coord of 6 Click to return to game board 30 Find the Vertex

x = -2(y - 4) Click to check answer (5, 4) Inside the function  move in same direction for y Outside the function  move in opp direction for x Click to return to game board 40 Find the vertex

x = -2y 2 - 8y - 1 Click 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

Compared to f(x) = | x|, g(x) = | x – 7| is shifted 7 units in this direction. Click to check answer Right Shifts inside a function move in the opposite direction Click to return to game board 10 Transformations

20 Transformations

30 Transformations

– 3 Every y-coordinate is flipped vertically and stretched by a multiple of 3 Click to return to game board 40 Transformations

Given that (2, 8) is on f(x) = x 3, 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

f(x) = – 3 | x | Click to check answer Even Graph has symmetry to y-axis Notice that f(-4) = f(4). Click to return to game board 10 Even, Odd or Neither

EVEN Parabola 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

x = - y 2 Click to check answer Neither Parabola 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

f(x) = – 3x 3 + x Click to check answer ODD Symmetry 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

f(x) = sin x Click to check answer 50 Even, Odd or Neither

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 axis Click to return to game board 10 More Parabolas

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 = y 2 or x = -y 2 Sideways so opens to the left or right. Click to return to game board 20 More Parabolas

Give the equation of a parabola that opens left with vertex (-3, 1) Click to check answer x = -a(y – 1) Any value of a as long as it is a negative number Click to return to game board 30 More Parabolas

Give the equation of a parabola that opens down with vertex (-7, -5) Click to check answer y = -a(x + 7) Any value of a as long as it is negative. Click to return to game board 40 More Parabolas

Find the vertex or graphing form of 4y + x = 2y Click to check answer x = 2(y – 1) Step 1: x = 2y 2 – 4y - 1 Step 2: x = 2(y 2 – 2y _____) – 1_______ Step 3: x = 2(y 2 – 2y +1 ) – Click to return to game board 50 More Parabolas

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