Parabola Transformation

Match the graph with the quadratic rule

Tags

CCSS.HSF-IF.C.7A

What transformation occurred to y = x² to y = (x - 5)² - 3?

• The graph translated right 5 units and down 3 units

• The graph translated right 3 units and down 5 units

• The graph translated left 5 units and down 3 units

• The graph translated left 3 units and up 5 units

What transformations have taken place to change the red graph into the blue graph?

• Reflected over x-axis, translated 3 right and 2 up.

• Reflected over y-axis, translated 3 right and 2 up.

• Reflected over x-axis, translated 2 right and 3 up.

• Rotated around (0, 0), translated 3 right and 2 up.

Caitlin graphs the function f(x) = ax², where a is a positive integer. If Caitlin multiplies a by -2, when compared to f(x), the new graph will become

• narrower and open downward

• narrower and open upward

• wider and open downward

• wider and open upward

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

• Vertical stretch by a factor of 5

• Vertical shrink/compress by a factor of 5

• Reflect over x-axis

• Vertical shift up 5 units

The graph of a quadratic function f is shown and the vertex is labeled with its coordinates.  If g(x) = f(x - 1) + 2, what is the minimum value of g?

* The minimum value of g is ​ (a)   because the minimum value of f is ​ (b)   and the graph of g is shifted ​ (c)   from the graph of f by ​ ​ (d)   .​

• 6

• 4

• up

• 2

• 1

• 3

• 5

• down

• left

• right

Explain the transformation

y= 1/2 ( x-4) ² +1

• thinner, right 4, up 1

• wider, left 4, up 1

• wider, right 4, down 1

• wider, right 4, up 1

Given f(x) = x² - 4 , how did we transform from the parent function?

• Horizontal shift left 4

• Vertical shift up 4

• Horizontal shift right 4

• Vertical shift down 4

The equation of red graph is y = x². What is the equation of the blue graph?

• y = (x + 5)²

• y = (x - 5)²

• y = x² - 5

• y = x² + 5

The graph of a transformed squaring function is shown below. Which equation and description best describes the graph? Select the equation ​ (a)   and description ​ (b)  

• neither even nor odd function

• even function

• odd function

Tags

CCSS.HSF.BF.B.3