Quadratic Transformations

The graph shows the function f(x)=x² in blue and another function g(x) in red.  Which could be the equation for g(x)?

• g(x)=3x²

• g(x)=1/3x²

• g(x) = x² - 3

• g(x) = (x-3)²

Move the correct answer to each box. Not all answers will be used. ( (a)   , ​ (b)   )

• 3

• -9

• -3

• 0

• 9

Tags

AI.9.7.C

"a" causes the parabola to vertically ​ (a)   when a < 1.

• compress

• stretch

Match the equation to its description.

• Reflected over x-axis and shifted up 4

• Reflected over x-axis and shifted down 4

• Reflected over x-axis and shifted right 4

• Reflected over x-axis and shifted left 4

• compress

• stretch

Given f(x) = -x² , how did we transform from the parent function?

• Horizontal shift left

• Reflection over the x-axis

• Vertical shift down

• Vertical compression

What is the axis of symmetry in the function f(x) = (x-1)² +2

• x = 1

• x = -1

• x = 2

• x = -2

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

Identify the vertex of f(x) = 5(x+6)² - 7

• (5,6)

• (0,0)

• (6,-7)

• (-6,-7)

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

• Shifted down 4 units

• Shifted left 4 units

• Shifted right 4 units

• Shifted up 4 units