Week 2 Quadratic Transformations Formative

Which answer choice correctly describes the transformations of the graph of the parent function  $f\left(x\right)=x^2$  to the graph of  $g\left(x\right)=\left(x+4\right)^2-5$  

• The graph of g is a translation of f moved 4 units down and 5 units left. 

• The graph of g is a translation of f moved 4 units right and 5 units down.

• The graph of g is a translation of f moved 4 units left and 5 units down. 

• The graph of g is a translation of f moved 4 units up and 5 units right. 

What is the equation of this graph? (Hint: Find the vertex to help you understand the translations from the parent function.)

• f(x) = (x -5)² + 1

• f(x) = (x - 1)² - 5

• f(x) = (x + 1)² - 5

• f(x) = (x + 5)² +1

If the graph of  $y=x^2$   is vertically stretched by 2, shifted 2 units left, and 5 units down, what is the new equation?

•  $y=-2\left(x-2\right)^2-5$  

•  $y=2\left(x\ +2\right)^2+\ 5$  

•  $y=2\left(x-5\right)^2-2$  

•  $y=2\left(x+2\right)^2-5$ 

What answer choice includes ALL the transformations of the graph  $y=x^2$  to become  $y=-\frac{1}{2}\left(x-4\right)^2+1$  ?

• 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

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

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

Tags

CCSS.HSF.BF.B.3

How did we transform from y=x^2?

y = -3x²

• reflection over the y-axis and a vertical shift 3 units down

• reflection over the x-axis and a vertical stretch by 3 (narrower)

• horizontal stretch by 3 (wider)

• vertical compression by -3 (wider)

Which quadratic function is represented by the graph?

• y = 2(x - 4)² + 5

• y = 2(x + 4)² + 5

• y = -2(x - 4)² + 5

• y = -2(x + 4)² + 5