Quadratics Transformations and Characteristics

Does this graph have a maximum or minimum value?

• maximum

• minimum

• neither

• both

Which function has a translation of 2 units right and a vertical stretch by a factor of 5?

• f(x)= 5(x - 2)²

• f(x) = 5(x + 2)²

• f(x) = (x - 2)² - 5

• f(x) = (x + 2)² + 5

What describes the effect on the graph of the equation y = 3x² when it is changed to y = -¾x²?

• The graph is congruent and is translated down.

• The graph is wider and opens downward.

• The graph is congruent and is translated up.

• The graph is narrower and opens downward.

How will the graph of f(x) = 3x² - 1 be affected if x² becomes (x - 2)^2?

• The vertex of the graph will move left 2 units.

• The vertex of the graph will move up 2 units.

• The vertex of the graph will move right 2 units.

• The vertex of the graph will move down 2 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

Which description best fits the transformation of f(x)=x² into f(x) =(x-5)²+3 ?

• Opens up, shifts to the right 5, and shifts up 3

• Is narrow, shifts left 5 and up 3

• Shifts right 5 and down 3

• Opens down and shifts up 3

• translates it left one unit and down 9 units

• translates it right one unit and down 9 units

• translates it up one unit and right 9 units

• translates it down one unit and left 9 units

• F

• G

• H

• J

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

How did we transform from y=x² to y = -3x²

• reflection in x-axis and shifts down

• reflection x-axis and narrower

• wider

• reflection x-axis and wider