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Algebra 1

7.17.6 Practice

Algebra 17.17.6 Practice
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Complete the following questions to practice the skills you have learned in this lesson.

  1. Here is the graph of quadratic function f .

Andre uses the expression ( x − 5 ) 2 + 7 to define f .

Noah uses the expression ( x + 5 ) 2 − 7 to define f .

Do you agree with either of them? 

  1. No
  2. Yes
  1. Here are the graphs of f ( x ) = x 2 , f ( x ) = x 2 − 5 , and f ( x ) = ( x + 2 ) 2 − 8 .

    1. How do the three graphs compare?
  1. All three graphs contain the point ( 0 , 0 ) .
  2. They all have a negative a coefficient in the vertex form of the equation.
  3. The shape is the same but they are in different locations.
  4. They all have the same vertex.
    1. Compare the graphs of f ( x ) = x 2 and f ( x ) = x 2 − 5 . What role does the -5 play in the comparison?
  1. Subtracting 5 from the squared term shifts the graph down by 5 units.
  2. Subtracting 5 from the squared term shifts the graph up by 5 units.
  3. Subtracting 5 from the squared term shifts the graph right by 5 units.
  4. Subtracting 5 from the squared term shifts the graph left by 5 units.
    1. Compare the graphs of f ( x ) = x 2 and f ( x ) = ( x + 2 ) 2 − 8 . What roles do the + 2 and − 8 play in the comparison?
  1. Adding 2 to x before squaring shifts the graph of f ( x ) = x 2 to the down by 2 units and subtracting 8 from the squared term shifts the graph right by 8 units.
  2. Adding 2 to x before squaring shifts the graph of f ( x ) = x 2 to the right by 2 units and subtracting 8 from the squared term shifts the graph up by 8 units.
  3. Adding 2 to x before squaring shifts the graph of f ( x ) = x 2 to the up by 2 units and subtracting 8 from the squared term shifts the graph left by 8 units.
  4. Adding 2 to x before squaring shifts the graph of f ( x ) = x 2 to the left by 2 units and subtracting 8 from the squared term shifts the graph down by 8 units.
  1. Select the three equations with a graph whose vertex has both a positive x and a positive y .
  1. f ( x ) = x 2
  2. f ( x ) = ( x − 1 ) 2
  3. f ( x ) = ( x − 3 ) 2 + 2
  4. f ( x ) = 2 ( x − 4 ) 2 − 5
  5. f ( x ) = 0.5 ( x + 2 ) 2 + 6
  6. f ( x ) = − ( x − 4 ) 2 + 3
  7. f ( x ) = − 2 ( x − 3 ) 2 + 1
  1. Which equation represents the graph shown?

    GRAPH OF A DOWNWARD PARABOLA WITH A VERTEX AT (NEGATIVE 7, 3
  1. f ( x ) = ( x − 7 ) 2 + 3
  2. f ( x ) = ( x + 7 ) 2 + 3
  3. f ( x ) = − ( x − 7 ) 2 + 3
  4. f ( x ) = − ( x + 7 ) 2 + 3
  1. The graph representing f ( x ) = x 2 is shifted 4 units to the left, 16 units down, and flipped so it opens downward (reflects over the x -axis). Which equation defines the curve?
  1. The graph of f ( x ) = x 2 is transformed by a horizontal dilation of 1 2 . What is the equation of the function that results from this translation? 
  1. f ( x ) = ( 1 2 x ) 2
  2. f ( x ) = ( x − 1 2 ) 2
  3. f ( x ) = x 2 + 1 2
  4. f ( x ) = 1 2 x 2
  1. A function g ( x ) = ( 2 x ) 2 − 5 was transformed from the parent quadratic function. Which of the following answer choices describes the transformations that were applied? 

Select the two descriptions that apply.

  1. A horizontal shift 2 units to the right
  2. A horizontal dilation by a factor of 2
  3. A horizontal shift left 5 units
  4. A vertical shift down 5 units
  5. A vertical dilation by a factor of 2
  1. Which of the following represents a function that has experienced a horizontal compression? 
  1. f ( x ) = x 2
  2. f ( x ) = ( 5 2 x ) 2
  3. f ( x ) = ( 1 5 x ) 2
  4. f ( x ) = ( − 1 x ) 2
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