Answer:
Yes, the equation y = -2x^2 + 1 is a function.
Explanation:
A function is a rule that assigns a unique output (y-value) to each input (x-value). In the given equation, we can see that for any given value of x, there is only one corresponding value of y.
To check this more formally, we can use the vertical line test. If a vertical line intersects a graph in more than one point, then the graph does not represent a function. If a vertical line intersects the graph in only one point, then the graph does represent a function.
The graph of the equation y = -2x^2 + 1 is a downward opening parabola. The vertex of the parabola is at (0,1). Since any vertical line intersects the graph at most once, we can conclude that the equation y = -2x^2 + 1 represents a function.