Quiz 7 :Transformations and Quadratic Equations

Aria is designing a parabolic arch for a garden entrance, modeled by f(x)=x². She decides to shift the arch two units to the right. Which equation describes the new position of the arch?

• x² + 2

• x² - 2

• (x + 2)²

• (x - 2)²

  James is designing a roller coaster track. The blue curve shows the original path of the track, modeled by the function f(x) = x³. He wants to shift the entire path to create a new track, shown by the red curve, g(x).  Which of the following is the correct equation for the new path, g(x)?

• g(x)=x³+1

• g(x)=x³-1

• g(x)=(x-1)³

• g(x)=(x+1)³

Tags

CCSS.HSF.BF.B.3

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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

Evelyn is designing a ramp for a playground. The shape of the ramp follows the graph shown above. Which of the following equations best represents the height of the ramp, h(x), in feet, as a function of the horizontal distance, x, in feet?

• h(x)= |x|+2

• h(x)= |x|-2

• h(x)= -|x|

• h(x)= -|x|+2

Which equation below is a quadratic function translated up 5 units?

• y = x² + 5
• y = (x + 5)²
• y = 5x²
• y = -x² - 5

• f(x) = −(x−2)³−1
• f(x) = −(x+2)³−1
• f(x) = −(x−2)³ + 1
• f(x) = −(x+2)³ + 1

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

If the blue graph is f(x) (the original function) and the red graph is the transformation, what is the equation of the red graph?

• -f(x)
• f(-x)
• f^-1(x)
• f(2x)

Kai is standing at the point (3, -2) on a map. He walks 5 units to the left and then 6 units up. What are the coordinates of Kai's new position?

• (2,-4)

• (-2,4)

• (8,4)

• (-2,-8)

Tags

CCSS.6.NS.C.8

Aiden is designing a parabolic arch for a bridge, modeled by f(x) = x². If he decides to double the height at every point by replacing it with 2⋅f(x), which transformation will occur to the arch?

• Vertical Compression by a factor of 2

• Vertical Stretch by a factor of 2

• Vertical translation up by 2 units.

• Reflection across the x-axis.