Quadratic Transformations H and K

If the blue graph is
f(x) = x² 
then the red must be...

Mathematical Equivalence

ON

• Reflection over x-axis

• None of these

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

Match the equation to its description.

• Vertically stretched by 2 and shifted up 4

• Vertically compressed by 2 and shifted up 4

• Vertically stretched by 2 and shifted left 4

• Vertically compressed by 2 and shifted left 4

If the blue is f(x)=x^2, then the red must be

• g(x)=x² - 5

• g(x)=x² + 5

• g(x)=(x - 5)²

• g(x)=(x + 5)²

In the vertex form f(x) = a(x - h)² + k , what does the 'h' value do?

• Shifts the function left or right

• Reflection over the x-axis

• Vertical stretch or compression

• Shifts the function up or down

Match the description to its equation.

• A

• B

• C

• D

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

• Compress by 2, shifted 2 units left and 5 down

• Stretch by 5, shifted 5 units left and 2 down

• Stretch by 2, shifted 2 units left and 5 down

• Compress by 5, shifted 2 units left and 2 down

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

• Vertically compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, vertically compressed by 1/2, shifted 4 units right and 1 unit up

• Reflected across x-axis, vertically stretched by 1/2, shifted 4 units left and 1 unit up

• Vertically stretched by 1/2, shifted 4 units right and 1 unit down

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

• shifted right 1 unit and up 4 units

• Shifted right 1 unit and down 4 units

• shifted left 1 unit and down 4 units

• shifted left 1 unit and up 4 units