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

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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