Zack sketches a parabola with a vertex at the origin that opens downward. What is the equation of Zack's function?
y = -x^2
100
y = (x+1)^2 - 5
Translated 1 unit left and 5 units down.
100
y = 3x^2 - 6
Vertically stretched by a factor of 3 and translated 6 units down.
100
f(x-7)
Translated 7 units right.
100
f(x) + 4
Translated 4 units up.
200
Dakota translates the quadratic parent function 10 units to the right and 4 units down. What is the equation of Dakota's function?
y = (x-10)^2 - 4
200
y = 1/6(x-3)^2 + 1
Vertically compressed, and translated 3 units to the right and 1 unit down.
200
y = (2x)^2 + 10
Horizontally compressed, and translated 10 units up.
200
f(x-3) + 21
Translated 3 units to the right and 21 units up.
200
2/3f(x)
Vertically compressed.
300
Gloria transforms the quadratic parent function by vertically stretching the parabola by a factor of 2. Then, she translates the parabola 8 units up and 6 units right. What is the equation of Gloria's parabola?
y = 2(x-6)^2 + 8
300
y = -4(x+2)^2 + 4
Reflected across the x-axis, vertically stretched, and translated 2 units to the left and 4 units up.
300
y = (6x+1)^2 + 9
Horizontally compressed and translated 1 unit left and 9 units up.
300
3f(x)
Vertically stretched.
300
f(1/5x) - 4
Horizontally stretched and translated 4 units down.
400
Makayla begins with the quadratic parent function. She reflects the parabola over the x-axis and translates the function 3 units to the left and 5 units down. What is Makayla's equation?
y = -(x+3)^2 - 5
400
y = -1/3(x)^2
Vertically compressed and reflected across the x-axis.
400
y = 5x^2
Vertically stretched
400
f(2/3x)
Horizontally stretched.
400
f(-x)
Reflected over the y-axis
500
A'Shantis transforms a quadratic function by stretching it vertically by a factor of 4 and translating the parabola 22 units down and 1 unit to the left. What is the equation of the transformed function?
y = 4(x+1)^2 - 22
500
y = (2x)^2 + 15
Horizontally compressed and translated 15 units up.
500
y = (2/5x)^2
Horizontally stretched.
500
-f(x)
Reflected over the x-axis.
500
8f(x-3) - 4
Vertically stretched and translated 3 units to the right and 4 units down.