ALGEBRA 2 - U7L1 QUADRATIC TRANSFORMATIONS

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

How did we transform from the parent function?
y = x² + 2

• horizontal shift up
• vertical shift up
• horizontal shift down
• vertical shift down

What is the vertex of this equation?

y = (x + 4)² -6

Pay attention to negative signs!

• (4, 6)

• (-4, -6)

• (-4, 6)

• (4, -6)

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

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

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

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

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

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

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 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

Find the equation of the parabola that has...

moved 3 units to the left

moved 5 units up

• $y=\left(x+3\right)^2+5$
  

• $y=\left(x+5\right)^2+3$

• $y=\left(x-3\right)^2+5$

• $y=\left(x+5\right)^2-3$

Find the equation of the parabola that has...

been stretched by 2

moved 5 units to the right

moved 3 units down

• $y=2\left(x-5\right)^2-3$

• $y=2\left(x+5\right)^2-3$

• $y=\frac{1}{2}\left(x+5\right)^2-3$

• $y=\frac{1}{2}\left(x-5\right)^2-3$

Given f(x) = (x + 6)² - 2 , how did we transform from the parent function?

• Horizontal shift left 6, vertical shift up 2

• Horizontal shift left 6, vertical shift down 2

• Horizontal shift right 6, vertical shift down 2

• Horizontal shift right 6, vertical shift up 2