Shifts and Transformations of Quadratics

Choose the equation of the quadratic function that is translated 6 units up, 2 units right, and is vertically stretched by a factor of 3 from the parent function.

• f(x) = 3(x - 2)²+6

• f(x) = 6(x + 2)²+3

• f(x) = 3(x + 2)² + 6

• f(x) = 6(x - 2)²-3

Choose the equation of the quadratic function that is reflected over the x-axis and translated down 3.

• f(x) = -x² + 3

• f(x) = -x² -3

• f(x) = -(x-3)²

• f(x) = -(x+3)²

Use transformations to identify the equation of the graph shown.

• f(x) = (x - 5)² - 2

• f(x) = (x + 5)² - 2

• f(x) = (x - 5)² + 2

• f(x) = (x + 5)² + 2

Use transformations to identify the equation of the graph shown.

• f(x) = (x + 3)² - 8

• f(x) = 3(x + 3)² - 8

• f(x) = (x - 3)² - 8

• f(x) = 2(x - 3)² - 8

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

• Wider

• Narrower

• Vertical translation up by 2 units.
• Reflection across the x-axis.

Which transformation will occur if f(x) = x² is replaced with f(x) + 2?

• Translation left 2 units

• Narrower

• Vertical translation up by 2 units.
• Reflection across the x-axis.

Which transformation will occur if f(x) = x² is replaced with -f(x)?

• Nothing happens, it stays the same.
• Narrower

• Vertical translation up by 2 units.
• Reflection across the x-axis.

f(x) is transformed so that it maps onto g(x). Which equation would correctly represent g(x)

• g(x)=f(x - 3)
• g(x)=f(x) - 3
• g(x)=f(x) + 3
• g(x)=3f(x)

What is the equation of the quadratic function obtained from vertically shrinking/compressing the parent function by 3/5 and then shifted up 8 units?

• f(x)= 3/5(x-8)²
• f(x)=3/5x²+8
• f(x)=x²
• f(x)=3/5x²-8

What is the equation of the quadratic function obtained from horizontally shifting the parent function 17 units left and then reflecting across the x-axis?

• f(x)= -x²-17
• f(x)= -(x-17)²
• f(x)= -(x+17)²
• f(x)= -x²+17