Identify the vertex and y-intercept of the graph of the function y = 3(x + 2)2 - 5.

vertex: (-2, -5) y-intercept: 7

Function Basics Review Quiz

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| By Nathan Kunkel

Nathan Kunkel

Community Contributor

Quizzes Created: 2 | Total Attempts: 634

Questions: 5 | Attempts: 81 | Updated: Apr 11, 2023

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Just a short 5 question quiz review basics of translating functions.

Questions and Answers

1.

Identify the vertex and y-intercept of the graph of the function y = 3(x + 2)² - 5.
- A.
  
  Vertex: (-2, -5) y-intercept: 7
- B.
  
  Vertex: (2, 5) y-intercept: 12
- C.
  
  Vertex: (2, -5) y-intercept: 7
- D.
  
  Vertex: (-2, 5) y-intercept: 1
Correct Answer
A. Vertex: (-2, -5) y-intercept: 7

Explanation
The vertex of a quadratic function in the form y = a(x - h)^2 + k is given by (h, k). In this case, the equation is y = 3(x + 2)^2 - 5, so the vertex is (-2, -5). The y-intercept is the value of y when x = 0. Plugging in x = 0 into the equation, we get y = 3(0 + 2)^2 - 5 = 3(4) - 5 = 12 - 5 = 7. Therefore, the y-intercept is 7.

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2.

Write the equation of the parabola in vertex form. vertex: (-2, 4), point: (2, 84)
- A.
  
  Y = 5(x - 2)² + 4
- B.
  
  Y = 84(x + 2)² - 4
- C.
  
  Y = 5(x + 2)²+4
- D.
  
  Y = 2(x - 2)² + 4
Correct Answer
C. Y = 5(x + 2)²+4

Explanation
The equation of a parabola in vertex form is given by y = a(x-h)^2 + k, where (h, k) represents the vertex of the parabola. In this case, the vertex is (-2, 4), so the equation should be of the form y = a(x + 2)^2 + 4. Since the given equation y = 5(x + 2)^2 + 4 matches this form, it is the correct answer.

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3.

Which quadratic function does the graph represent?
- A.
  
  F(x) = -x² + 6x + 7
- B.
  
  F(x) = x² + 6x - 7
- C.
  
  F(x) = -x² + 6x - 7
- D.
  
  F(x) = -x² - 6x - 7
Correct Answer
C. F(x) = -x² + 6x - 7

Explanation
The given quadratic function is f(x) = -x^2 + 6x - 7. This can be determined by analyzing the coefficients of the quadratic equation. The quadratic term has a negative coefficient, indicating that the graph opens downwards. The linear term has a positive coefficient, indicating that the graph has a positive slope. The constant term is negative, indicating that the graph intersects the y-axis below the origin. Therefore, the correct answer is f(x) = -x^2 + 6x - 7.

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4.

Use vertex form to write the equation of the parabola.
- A.
  
  Y = 2(x - 3)² - 2
- B.
  
  Y = 2(x + 3)² - 2
- C.
  
  Y = 2(x + 3)² + 2
- D.
  
  Y = (x - 3)² - 2
Correct Answer
A. Y = 2(x - 3)² - 2

Explanation
The given equation is in the vertex form of a parabola, which is y = a(x - h)^2 + k. In this equation, the vertex of the parabola is represented by the point (h, k).

Comparing the given equation y = 2(x - 3)^2 - 2 with the vertex form, we can see that the vertex of the parabola is at the point (3, -2). The coefficient "2" in front of the (x - 3)^2 term indicates that the parabola is stretched vertically. Since the coefficient is positive, the parabola opens upward. Therefore, the equation y = 2(x - 3)^2 - 2 represents a parabola with its vertex at (3, -2), opening upward, and stretched vertically.

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5.

The parent function f(x) = x² is reflected across the x-axis, vertically stretched by a factor of 3, and translated right 7 units to create g. Use the description to write the quadratic function in vertex form.
- A.
  
  G(x) = 7(x + 3)²
- B.
  
  G(x) = -3(x - 7)²
- C.
  
  G(x) = -3(x + 7)²
- D.
  
  G(x) = 3(x - 7)²
Correct Answer
B. G(x) = -3(x - 7)²

Explanation
The parent function f(x) = x^2 is reflected across the x-axis, vertically stretched by a factor of 3, and translated right 7 units to create g. The equation g(x) = -3(x - 7)^2 represents this transformation. The negative sign indicates the reflection across the x-axis, the coefficient -3 represents the vertical stretch, and the (x - 7)^2 term represents the translation right 7 units. Thus, the correct answer is g(x) = -3(x - 7)^2.

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Current Version
Apr 11, 2023

Quiz Edited by
ProProfs Editorial Team
Apr 06, 2020

Quiz Created by
Nathan Kunkel

Function Basics Review Quiz

Identify the vertex and y-intercept of the graph of the function y = 3(x + 2)2 - 5.

Write the equation of the parabola in vertex form. vertex: (-2, 4), point: (2, 84)

Which quadratic function does the graph represent?

Use vertex form to write the equation of the parabola.

The parent function f(x) = x2 is reflected across the x-axis, vertically stretched by a factor of 3, and translated right 7 units to create g. Use the description to write the quadratic function in vertex form.

Identify the vertex and y-intercept of the graph of the function y = 3(x + 2)² - 5.

The parent function f(x) = x² is reflected across the x-axis, vertically stretched by a factor of 3, and translated right 7 units to create g. Use the description to write the quadratic function in vertex form.