quadratic transformations

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

Identify the vertex of f(x) = -2(x+1)² + 3

• (h,k)

• (3, 1)

• (-1,-3)

• (-1,3)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

Tags

CCSS.HSF.BF.B.3

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

Tags

CCSS.HSF.BF.B.3

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

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

Given f(x) = ax² , if a > 1 , the graph will transform by

• becoming wider or vertically compressed

• becoming narrower or vertically stretched

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

Find the equation of the parabola that has...

moved 3 units to the left

moved 5 units up

• $y=\left(x+3\right)^2+5$
  

• $y=\left(x+5\right)^2+3$

• $y=\left(x-3\right)^2+5$

• $y=\left(x+5\right)^2-3$

Tags

CCSS.HSA.CED.A.2

CCSS.HSF.BF.B.3

Find the equation of the parabola that has...

been reflected

stretched by 5

• $y=-5x^2$

• $y=-\frac{1}{5}x^2$

• $-y=5x^2$

• $-y=\frac{1}{5}x^2$

Tags

CCSS.HSF.BF.B.3

Find the equation of the parabola that has...

been stretched by 2

moved 5 units to the right

moved 3 units down

• $y=2\left(x-5\right)^2-3$

• $y=2\left(x+5\right)^2-3$

• $y=\frac{1}{2}\left(x+5\right)^2-3$

• $y=\frac{1}{2}\left(x-5\right)^2-3$

Tags

CCSS.HSF.BF.B.3

Which of the following is the correct equation for the given graph?

• f(x) = (x - 2)² - 1
• f(x) = (x + 2)² - 1
• f(x) = -(x + 2)² - 1
• f(x) = -(x - 2)² - 1

Tags

CCSS.HSF-IF.C.7A