What is the Vertex?
y = x2
(0,0)
y = x2 + 7
Moved 7 units up
a = 2, h = 1, k = 3
y = 2(x - 1)2 + 3
a > 0 and the vertex is (1, 1)
minimum at 1
Increasing to the right of x = 2 and decreasing to the left of x = 2
Increasing x > 2 Decreasing x < 2
y = (x-1)2
(1,0)
y = -(x + 2)2
Flipped over the x- axis and moved 2 units left
a = -1, h = -2, k = -3
y= -(x + 2)2 - 3
maximum at 0
a > 0 vertex is (1, -3)
Increasing x > 1 Decreasing x < 1
y = 2(x+3)2 - 1
(-3, 1)
y = 2x2 - 9
Vertically stretched by a factor of 2 and moved 9 units down
vertically stretched by a factor of 4 and moved 8 units down
y = 4x2 - 8
y = 2(x +1)2 - 5
Minimum at -5
a < 0 vertex is (-3, 2)
Increasing x < -3 Decreasing x > -3
y = 1/2(x - 3)2 + 4
(3, 4)
y = 3(x - 8)2 + 2
Vertically stretched by a factor of 3 moved 8 units to the right and moved 2 units up
shrunk by a factor of 1/3, moved 7 units to the right and 1 unit up.
y = 1/3(x - 7)2 + 1
y = -1/2x2 + 6
Maximum at 6
y = -6(x + 2)2 -3
Increasing x < -2 Decreasing x > -2
y = 2x2 - 13
(0, -13)
y = -0.5(x + 2)2 -4
Flipped over the x-axis, shrunk by a factor of 0.5, moved 2 units to the left, moved 4 units down
reflected over the x-axis, vertically stretched by a factor of 5 and moved 4 units to the left
y = -5(x + 4)2
y = -4(x + 5)2 - 1
Maximum at -1
y = x2 + 2
Increasing x > 0 Decreasing x < 0