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What is the range of the function y = -x^2 + 4?

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Question: What is the range of the function y = -x^2 + 4?

Options:

  1. y ≤ 4
  2. y ≥ 4
  3. y < 4
  4. y > 4

Correct Answer: y ≤ 4

Solution: 

The vertex is at (0, 4) and opens downwards, so the range is y ≤ 4.

What is the range of the function y = -x^2 + 4?

Practice Questions

Q1
What is the range of the function y = -x^2 + 4?
  1. y ≤ 4
  2. y ≥ 4
  3. y < 4
  4. y > 4

Questions & Step-by-Step Solutions

What is the range of the function y = -x^2 + 4?
  • Step 1: Identify the function, which is y = -x^2 + 4.
  • Step 2: Recognize that this is a quadratic function in the form of y = ax^2 + bx + c.
  • Step 3: Note that the coefficient of x^2 (which is -1) is negative, meaning the parabola opens downwards.
  • Step 4: Find the vertex of the parabola. For the function y = -x^2 + 4, the vertex is at (0, 4).
  • Step 5: Understand that since the parabola opens downwards, the highest point (the vertex) is the maximum value of y.
  • Step 6: Conclude that the maximum value of y is 4, and since the parabola opens downwards, y can take any value less than or equal to 4.
  • Step 7: Write the range of the function as y ≤ 4.
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