Quadratic Transformation

Quadratic Transformation

Horizontal Shift

 $f\left(x\right)=a\left(bx-h\right)^2+k$  

Multiple Choice

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)=f(x) - 2

Multiple Choice

Given f(x) = (x + 3)² , how did we transform from the parent function?

• Horizontal shift left 3

• Vertical shift up 3

• Horizontal shift right 3

• Vertical shift down 3

Multiple Choice

Which transformation maps the graph of

f(x) = x² to the graph of g(x) = (x + 4)²?

• a reflection across the line x = -4

• a reflection across the line y = -4

• a translation shifting f(x) 4 units to the left

• a translation shifting f(x) 4 units to the right

Vertical Shift

 $f\left(x\right)=a\left(bx-h\right)^2+k$  

Multiple Choice

How did we transform from the parent function?

y = x² + 2

• horizontal shift up

• vertical shift up

• horizontal shift down

• vertical shift down

Multiple Choice

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

Multiple Choice

What steps transform the graph y = x² to y = x² + 8

• shifted up 8 units

• shifted down 8 units

• shifted left 8 units

• shifted right 8 units

Vertical Stretch/Compression

 $f\left(x\right)=a\left(bx-h\right)^2+k$  

Multiple Choice

Does the equation vertically stretch, compress, or reflect?
 $f\left(x\right)=\frac{1}{4}x^2$  
*Always compare to the parent function (graph first)*

• Stretch by a factor of  $\frac{1}{4}$  

• Compress by a factor of  $\frac{1}{4}$  

• Reflect across the x-axis

• Both Compress by a factor of 2 & Reflect across the x-axis

Multiple Choice

Does the equation vertically stretch, compress, or reflect?

 $f\left(x\right)=\ 2x^2$  
*Always compare to the parent function (graph first)*

• Stretch by a factor of 2

• Compress by a factor of 2

• Reflect across the y-axis

• Both Stretch by a factor of   $\frac{1}{2}$  & Reflect across the x-axis

Multiple Choice

Does the equation vertically stretch, compress, or reflect?

 $f\left(x\right)=0.75x^2$  
*Always compare to the parent function (graph first)*

• Stretch by a factor of 2

• Compress by a factor of 0.75

• Reflect across the x-axis

• Both stretch by a factor of 2 and reflect across the x-axis

Horizontal Stretch/Compression

 $f\left(x\right)=a\left(bx-h\right)^2+k$  

Multiple Choice

Given f(x) = (2x + 3)² , how did we transform from the parent function?

• Horizontal compression of 2

• Vertical compression of 2

• Horizontal stretch of 2

• Vertical stretch of 2

Multiple Choice

Given f(x) = (0.5x + 3)² , how did we transform from the parent function?

• Horizontal compression of 0.5

• Vertical compression of 0.5

• Horizontal stretch of 0.5

• Vertical stretch of 0.5

Multiple Choice

Given

 $f\left(x\right)=\left(\frac{1}{4}x-1\right)^2+1$ how did we transform from the parent function?

• Horizontal compression of 1/4

• Vertical compression of 1/4

• Horizontal stretch of 1/4

• Vertical stretch of 1/4

Reflection

 $f\left(x\right)=a\left(bx-h\right)^2+k$  

Multiple Choice

What is the equation for the following:

The graph of y=x² has a vertical stretch by 5, a horizontal stretch by 0.5, a horizontal shift 6 units left, and has a vertical shift 3 units up.

• y = 5(0.5x + 6)² + 3

• y = 5(0.5x - 6)² + 3

• y = 0.5(5x + 6)² + 3

• y = 0.5(x - 6)² + 3

Multiple Choice

Write an equation for the following:

The graph of y=x² has a vertical compression of 0.8, reflects over the x-axis, has a horizontal shift 8 units to the right, and has a vertical shift of 2 units up.

• y = 0.8(x+8)² + 2

• y = - 0.8(x+8)² + 2

• y = 0.8(x - 8)² + 2

• y = - 0.8(x - 8)² + 2

Multiple Choice

Write an equation for the following:

The graph of y=x² has a horizontal stretch with a scale factor of 0.3, a vertical shift 4 units up, and reflects over the x-axis.

• y = (0.3x - 4)²

• y = - (0.3x - 4)²

• y = - (0.3x)² + 4

• y = - 0.3x² + 4

Multiple Choice

Write an equation for the following:

The graph of y=x² has a vertical stretch by a scale factor of 2, has a horizontal shift 5 units right, and has a vertical shift 3 units down.

• y = (2x - 5)² - 3

• y = 2(x - 5)² - 3

• y = (2x + 5)² - 3

• y = 2(x + 5)² - 3

Multiple Choice

Describe the transformation:

y= - ¾ (x - 7)² + 3

• Vertical stretch, up 3, right 7

• Vertical stretch, down 7, right 3, reflection

• Vertical compression, up 3, left 7, reflection

• Vertical compression, up 3, right 7, reflection

Multiple Choice

What transformation occurred to create the green parabola from the red parabola, y = x²?

• y = 0.5(x+2)² - 3

• y = 2(x-2)² - 3

• y = 2(x+2)² - 3

• y = 0.5(x-2)² - 3

Multiple Choice

What transformation occurred to create parabola from the purple parabola?

• y = - (x-3)² + 6

• y = - 0.5(x-3)² + 6

• y = - 2(x-3)² + 6

• y = - 0.5(x+3)² + 6