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Practice

9.11.5 Practice

9.11.5 • Practice

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

  1. Here is a graph of a quadratic function f ( x ) . What is the minimum value of f ( x ) ?

  1. The graph that represents f ( x ) = ( x + 1 ) 2 − 4 has its vertex at ( − 1 , − 4 ) .

Explain how we can tell from the expression ( x + 1 ) 2 − 4 that − 4 is the minimum value of f rather than the maximum value.

  1. The coefficient of the quadratic term is positive; therefore, the vertex will be a minimum value.
  2. We cannot tell from the expression; we have to graph it.
  3. The expression ( x + 1 ) 2 is a squared expression, so its value will always be positive or zero.
  4. The constant is always the minimum value.
  1. g ( x ) = ( x − 5 ) 2 + 6 defines a quadratic function. Find the vertex of the graph of the function. Then, state whether the vertex corresponds to the maximum or the minimum value of the function.
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Does the vertex correspond to the maximum or the minimum value of the function?
  1. Minimum
  2. Maximum
  1. h ( x ) = ( x + 5 ) 2 − 1 defines a quadratic function. Find the vertex of the graph of the function. Then, state whether the vertex corresponds to the maximum or the minimum value of the function.
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Does the vertex correspond to the maximum or the minimum value of the function?
  1. Minimum
  2. Maximum
  1. f ( x ) = − 2 ( x + 3 ) 2 − 10 defines a quadratic function. Find the vertex of the graph of the function. Then, state whether the vertex corresponds to the maximum or the minimum value of the function.
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Does the vertex correspond to the maximum or the minimum value of the function?
  1. Minimum
  2. Maximum
  1. p ( x ) = 3 ( x − 7 ) 2 + 11 defines a quadratic function. Find the vertex of the graph of the function. Then, state whether the vertex corresponds to the maximum or the minimum value of the function.
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Does the vertex correspond to the maximum or the minimum value of the function?
  1. Minimum
  2. Maximum
  1. g ( x ) = − ( x − 2 ) 2 − 2 defines a quadratic function. Find the vertex of the graph of the function. Then, state whether the vertex corresponds to the maximum or the minimum value of the function.
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Does the vertex correspond to the maximum or the minimum value of the function?
  1. Minimum
  2. Maximum
  1. h ( x ) = ( x + 1 ) 2 defines a quadratic function. Find the vertex of the graph of the function. Then, state whether the vertex corresponds to the maximum or the minimum value of the function.
  1. What is the x -coordinate of the vertex?
  1. What is the y -coordinate of the vertex?
  1. Does the vertex correspond to the maximum or the minimum value of the function?
  1. Minimum
  2. Maximum
  1. A backyard farmer wants to enclose a rectangular space for a new garden within her fenced backyard. She has purchased 80 feet of wire fencing to enclose three sides, and she will use a section of the backyard fence as the fourth side. The function is graphed below. What is the maximum area, in square feet, that can be fenced in?

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