Quadratic Transformations

Quadratic Transformations

You will learn how to identify changes to a PARABOLA when changing values from its function.

Parent Function

Parent Quadratic function y=x²

The simplest form of a quadratic equation.

a=1 (y=1x²)

Shift Up or Shift Down

• When we add to C, the parabola shifts up.

• When we subtract C, the parabola shifts down.

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

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

How would the graph of the function y = x² + 4 be affected if the function were   changed to y = x² + 1?

• The graph would shift 3 units up.   
• The graph would shift 3 units down.
• The graph would shift 3 units right.   
• The graph would shift 3 units right.

Multiple Choice

What would the equation for the new quadratic function be if it was vertically shifted up 3 units from the function f(x)=4x²+2?

• g(x)=x²+3

• g(x)=7x²+2

• g(x)=4x²+3

• g(x)=4x²+5

Open Up/Open Down

Multiple Choice

A quadratic is reflected down when the value of a is negative.

• TRUE

• FALSE

Multiple Choice

Will there be a reflection from graph y = x ² - 7 to the graph y =x²

• True

• False

Multiple Choice

Will there be a reflection from graph f(x) = x² to the graph of g(x) = -x²

• True

• False

Multiple Choice

Given f(x) = -x² , how did we transform from the parent function?

• Horizontal shift left

• Reflection over the x-axis

• Vertical shift down

• Vertical compression

Narrow or Wider

• The bigger the a, the narrower the parabola. Also called a stretch.

• The smaller the a, the wider the parabola. Also called a compression.

• Reflection does not affect the width of the parabola.

Multiple Choice

Given $$f\left(x\right)=\frac{1}{4}x²$$  how did we transform from the parent function?

• Vertical compression (wider)

• Vertical stretch (narrower)

• Shift down

• reflection over x-axis

Multiple Choice

How is the graph of y = x² different from the graph of
y = 1/3x²?

• The graph of
  y = 1/3x² is shifted up.
• The graph of
  y = 1/3x² is shifted down.
• The graph of
  y = 1/3x² is wider.
• The graph of
  y = 1/3x² is narrower.

Multiple Choice

Which quadratic would be the narrowest?

• $$f\left(x\right)=\frac{1}{2}x^2$$

• $$f\left(x\right)=x^2$$

• $$f\left(x\right)=3x^2$$

• $$f\left(x\right)=5x^2$$

Multiple Choice

Which list orders the quadratic functions from narrowest to widest?

• y = x²

  y = 4x²

  y = 2x² - 2

  y = 0.5 x²

• y = 0.5 x²

  y = x²

  y = 2x² - 2

  y = 4x²

• y = 4x²

  y = 2x² - 2

  y = x²

  y = 0.5 x²

• y = 2x² - 2

  y = 4x²

  y = 0.5x²

  y = x²

Multiple Choice

How did we transform from y=x²

-------> y = $$\frac{1}{5}$$  x²-2

• vertical reflection and vertical shift down

• vertical Compression

  and shift down

• Vertical stretch and shift up

• reflection and vertical compression

Multiple Choice

How did we transform from y=x²

-------> y =-3x²+4

• Vertical Stretched by 2 and translation up 4
•  Vertical Compressed by 2 and translation up 4
• Horizontal Stretched by 2 and translation left 4
• Horizontal Compressed by 2 and translation right 4