Quadratic Transformations

What is the vertex form of a quadratic function?

• f(x) = 2a(x-h)² + k

• f(x) = a(x-h)² + k

• f(x) = (x+h)² + k

• f(x) = a(x-h) - k

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.A.1

CCSS.HSF.IF.C.8

Identify the vertex of f(x) = -2(x+1)² + 3

• (h,k)

• (3, 1)

• (-1,-3)

• (-1,3)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What steps transform the graph y = x² to y = 2(x+2)² - 5?

• Wider by 2, translated 2 units left and 5 down

• Narrower by 5, translated 5 units left and 2 down

• Narrower by 2, translated 2 units left and 5 down

• Wider by 5, translated 2 units left and 2 down

What steps transform the graph y = x² to y = -1/2(x-4)² + 1?

• Wider by 1/2, translated 4 units right and 1 unit up

• Reflected across x-axis, wider by 1/2, translated 4 units right and 1 unit up

• Reflected across x-axis, narrower by 1/2, translated 4 units left and 1 unit up

• Narrower by 1/2, translated 4 units right and 1 unit down

What steps transform the graph y = x² to y = x² + 8

• translated up 8 units

• translated down 8 units

• translated left 8 units

• translated right 8 units

What steps transform the graph y = x² to y = (x - 4)²

• translated down 4 units

• translated left 4 units

• translated right 4 units

• translated up 4 units

Which transformation maps the graph of
f(x) = x² to the graph of g(x) = (x + 4)²?

• a reflection across the line x = -4
• a reflection across the line y = -4
• a translation shifting f(x) 4 units to the left
• a translation shifting f(x) 4 units to the right

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

Match the equation to its description.

• Narrower by 2 and shifted up 4

• Wider by 2 and shifted up 4

• Narrower by 2 and shifted left 4

• Wider by 2 and shifted left 4

Match the equation to its description.

• Reflected over x-axis and translated up 4

• Reflected over x-axis and translated down 4

• Reflected over x-axis and translated right 4

• Reflected over x-axis and translated left 4

Match the equation to its description.

• Narrower by 4 and translated up 4

• Wider by 4 and translated up 4

• Narrower by 4 and translated right 4

• Wider by 4 and translated right 4