and . Which statement is true?

g(x) and f(x) have the same vertex

g(x) and f(x) have different axes of symmetry

9.1-9.4 Quiz

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| By Mrsmosher

Mrsmosher

Community Contributor

Quizzes Created: 16 | Total Attempts: 21,089

Questions: 10 | Attempts: 192 | Updated: Mar 21, 2023

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Questions and Answers

1.

Which is a quadratic function?
- A.
- B.
- C.
- D.
Correct Answer
B.

Explanation
A quadratic function is a function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0. Quadratic functions have a degree of 2 and their graphs form a parabola. Therefore, the correct answer is any function that can be expressed in this form.

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2.

Which function has a graph that opens downward?
- A.
- B.
- C.
- D.
Correct Answer
C.

Explanation
The function that has a graph that opens downward is a quadratic function with a negative leading coefficient. In a quadratic function, the highest power of the variable is 2, and the leading coefficient determines the direction of the graph. When the leading coefficient is negative, the graph opens downward, forming a concave shape.

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3.

What is the vertex of the parabola graphed below?
- A.
  
  (-3,0)
- B.
  
  (-4,-1)
- C.
  
  (1,0)
- D.
  
  (-1,-4)
Correct Answer
D. (-1,-4)

Explanation
The vertex of a parabola is the point where the parabola reaches its minimum or maximum value. In this case, the vertex is given as (-1,-4), which means the parabola is at its lowest point at x = -1 and y = -4.

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4.

What are the zeros of the function graphed below?
- A.
  
  -1 and 0
- B.
  
  -2 and 0
- C.
  
  0 and 1
- D.
  
  0 and 2
Correct Answer
B. -2 and 0

Explanation
The zeros of a function are the values of x where the function equals zero. In the given graph, we can see that the graph intersects the x-axis at x = -2 and x = 0. This means that the function equals zero at these two points. Therefore, the zeros of the function are -2 and 0.

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1
0
5.

What is the vertex of the graph of ?
- A.
  
  (2, 5)
- B.
  
  (-2, -27)
- C.
  
  (-2, 5)
- D.
  
  (4, -11)
Correct Answer
A. (2, 5)

Explanation
The vertex of a graph represents the highest or lowest point on the graph. In this case, the vertex is given as (2, 5), which means that the highest or lowest point on the graph is at the coordinates (2, 5).

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6.

What function is shown on the graph below?
- A.
- B.
- C.
- D.
Correct Answer
B.
7.

The height in feet of a rocket launched from the ground can be modeled by the function , where x is the time in seconds after it is launched. What is the rocket’s maximum height?
- A.
  
  144 feet
- B.
  
  240 feet
- C.
  
  288 feet
- D.
  
  432 feet
Correct Answer
A. 144 feet

Explanation
The rocket's maximum height is 144 feet because it is stated in the answer section. However, without additional information or the actual function, it is not possible to determine the rocket's maximum height based solely on the given question.

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8.

Which function's graph has an axis of symmetry of x=2?
- A.
- B.
- C.
- D.
Correct Answer
D.

Explanation
The function that has a graph with an axis of symmetry of x=2 is a quadratic function in the form of f(x) = (x - 2)^2. The axis of symmetry of a quadratic function is the vertical line that passes through the vertex of the parabola. In this case, the vertex is at (2, 0) which means the axis of symmetry is x=2.

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9.

and . Which statement is true?
- A.
  
  G(x) is wider than f(x)
- B.
  
  G(x) is narrower than f(x)
- C.
  
  G(x) and f(x) have the same vertex
- D.
  
  G(x) and f(x) have different axes of symmetry
Correct Answer
B. G(x) is narrower than f(x)
10.

Which function has a vertex different from the vertex of the graph of
- A.
- B.
- C.
- D.
Correct Answer
A.