Aiden is designing a parabolic arch for a bridge, modeled by f(x) = x 2 . 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 Stretch by a factor of 2

Vertical Compression by a factor of 2

Vertical translation up by 2 units.

What are the following transformations: f(-x) - 4

reflection over the y axis and 4 units down

reflection over the x axis and 4 units right

reflection over the x axis and 4 units down

reflection over the y axis and 4 units right

Describe the transformations that maps y = g(x) to y = - g(x + 6) - 10

Reflect over x-axis Shifted down 10 units Shifted left 6 units

Reflect over y-axis Shifted down 10 units Shifted left 6 units

Reflect over x-axis Shifted up 10 units Shifted left 6 units

Reflect over y-axis Shifted up 10 units Shifted right 6 units

Jackson is looking at the graph of a parabola representing the path of a ball he threw. He notices a green dashed line that divides the parabola into two mirror images. What is the green dashed line called?

Axis of symmetry / Line of symmetry

Aria is designing a parabolic arch for a garden. The equation she uses is f(x) = a(x - h)² + k, where changing the 'a' value affects the shape of the arch. What does the 'a' value do?

Changing 'a' value has no affect on the arch

In the equation y= ax 2 + bx + c , if a > 0, then...

the graph of the parabola will open up

the graph of the parabola will have a maximum.

the graph of the parabola will open down

What is the arrow pointing at? How can you use this value to determine the minimum/maximum values?

The arrow is pointing at the vertex. The y value is equivalent to the minimum/maximum

The arrow is pointing at the y-intercept. The y value of this point is equivalent to the maximum/minimum

The arrow is pointing at the vertex. The x value of this point is equivalent to the maximum/minimum

The arrow is pointing at the solution. The y value of this point is equivalent to the maximum and the x value is equivalent to the minimum

Does the following quadratic equation have a maximum or minimum value? How can you tell? y=x²+2x-3

Minimum value, because the value of a is positive

Maximum value, because the value of b is positive

Maximum value, because the value of a is positive

Minimum value, because the value of c is negative

The axis of symmetry line passes through which point?

symmetrical point for the vertex

Which statement best explains why vertex form is helpful when graphing?

It shows the vertex and direction of opening directly.

It reveals the intercepts immediately.

It gives the slope and y-intercept.

It hides transformations to make the equation simpler.

Which of the following represents a real-world context best modeled by a quadratic function?

The height of a ball thrown upward over time

The cost of a taxi ride with a flat rate plus a per-mile charge

The number of bacteria doubling every hour

The depreciation of a car’s value over years

A student claims the graph of $$y=(x−1)^2−9$$ has its vertex at (-1, -9). Why is this incorrect?

The vertex should be at (1, -9) because of the minus sign inside the parentheses.

The vertex should be at (-1, 9) because the minus affects both coordinates.

The vertex is always at the origin.

The student used the wrong direction for vertical movement.

What are the transformations to the graph compared to the parent function?

Shifted right 2, shifted up 3, and reflected over the x-axis

Shifted right 2, shifted up 3, and reflected over the y-axis

Shifted left 2, shifted up 3, and reflected over the y-axis

Shifted left 2, shifted up 3, and reflected over the x-axis

What is a vertical stretch in transformations?

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

A vertical stretch occurs when the input values of a function are multiplied by a factor greater than 1, making the graph wider.

A vertical stretch occurs when the graph is flipped upside down, inverting the function's output values.

A vertical stretch occurs when the function's output values are decreased, making the graph shorter.

Describe the transformation: $$f(x) = \frac{4}{5}|x+5|+2$$

Vertical shrink by a factor of 4/5, shifts left 5 units, and shifts up 2 units.

Vertical stretch by a factor of 5/4, shifts right 5 units, and shifts down 2 units.

No transformation, the function remains the same.

Vertical shrink by a factor of 4, shifts left 5 units, and shifts up 2 units.

The growth of Able is measured by the function a(x) . Micah's growth is modeled by m(x) = 1.5 a(x) . How does Micah's growth compare with Able's growth?

Micah is growing 1.5 times faster than Able

Able is growing 1.5 times faster than Micah

Micah is 1.5 feet taller than Able

Micah will always be 1.5 feet taller than Able

Quiz: Transformations

Authored by Kathy Binondo

Mathematics

10th Grade

CCSS covered

Used 3+ times

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

.
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 QUESTION

5 mins • 1 pt

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

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

y = x² + 5

y = (x + 5)²

y = 5x²

y = -x² - 5

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

f(x) = −(x−2)³−1

f(x) = −(x+2)³−1

f(x) = −(x−2)³ + 1

f(x) = −(x+2)³ + 1

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

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

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Quiz: Transformations

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?

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)?

.
If the blue is f(x)=x^2,then the red must be

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?

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

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

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?

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?

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?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Quiz: Transformations

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?

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)?

. If the blue is f(x)=x2, then the red must be

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?

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

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

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?

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?

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?

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

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?

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)?

.
If the blue is f(x)=x^2,then the red must be

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

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?