Week 25 Quadratic Transformations (pgs. 1-4)

Choose the quadratic that represents a vertical compression.

•  $f\left(x\right)\ =\ 5x^2$  

•  $y\ =\ \frac{2}{3}x^2$  

•  $y\ =\ \frac{4}{3}x^2$  

•  $f\left(x\right)\ =\ 1.2x^2$  

Choose the quadratic that represents a vertical stretch.

• $y\ =\ 5x^2$

• $f\left(x\right)\ =\ \frac{2}{5}x^2$

• $y\ =\ \ \frac{1}{8}x^2$

• $f\left(x\right)\ =\ 0.75x^2$

Choose the quadratic that has been vertically stretched by a factor of 2, shifted right 3 units, and shifted up 4 units.

• $f\left(x\right)\ =\ 2\left(x+3\right)^2+4$

• $f\left(x\right)\ =\ -2x^2+4$

• $y\ =\ 2\left(x-4\right)^2+3$

• $f\left(x\right)\ =\ 2\left(x-3\right)^2+4$

Choose the quadratic that has a vertical compression of a factor of 1/2, is reflected across the x-axis, and is shifted left 5 units.

• $y\ =\ -\frac{1}{2}\left(x-5\right)^2$

• $f\left(x\right)\ =\frac{1}{2}\left(x+5\right)^2$

• $f\left(x\right)\ =\ -\frac{1}{2}\left(x+5\right)^2$

• $f\left(x\right)\ =\ -\frac{1}{2}x^2+5$

Choose the quadratic that is a reflection across the x-axis and a vertical shift of -8 units.

• $f\left(x\right)\ =\ -x-8$

• $f\left(x\right)\ =\ -x^2-8$

• $f\left(x\right)\ =\ -\left(x-8\right)^2$

• $f\left(x\right)\ =\ x^2-8$

Describe the transformation:

 $f\left(x\right)\ =\ 7x^2+9$  

• Vertical stretch by a factor of 7, and a vertical shift of -9 units

• Vertical compression by a factor of 7, and a vertical shift of -9 units

• Vertical stretch by a factor of 7, and a vertical shift of 9 units

• Vertical compression by a factor of 7, and a vertical shift of 9 units

Describe the transformation:

 $f\left(x\right)\ =\ -\frac{1}{5}\left(x+6\right)^2-3$  

• reflection across the x-axis; vertical compression of a factor of 1/5; horizontal translation of -6 units; vertical translation of -3 units

• reflection across the x-axis; vertical stretch of a factor of 1/5; horizontal translation of 3 units; vertical translation of 6 units

• reflection across the x-axis; vertical compression of a factor of 1/5; horizontal translation of 6 units; vertical translation of 3 units

• reflection across the x-axis; vertical stretch of a factor of 1/5; horizontal translation of -6 units; vertical translation of 3 units

What is the vertex?

 $f\left(x\right)\ =\ x^2$  

• (2,2)

• (1,1)

• (2,4)

• (0,0)

What is the vertex?

 $f\left(x\right)\ =3\ x^2+12$  

• (3, -12)

• (0, 12)

• (12, 0)

• (-12, 0)

• (3, -12)

Find the axis of symmetry:

 $2x^2-8x+12$  

• x = 2

• x = -8

• x = 12

• none of these