Y=-x²+1

To prepare for an exam on this equation, there are several things you can do. Here are some steps that can help you understand and analyze the equation y = -x^2 + 1:

1. Understand the basic form: The equation is in the form of a quadratic function, where the highest power of the variable (x) is 2. The general form of a quadratic function is y = ax^2 + bx + c.

2. Identify the coefficients: In this equation, the coefficient "a" is -1, which means the parabola opens downwards. The coefficient "b" is 0, indicating that there is no linear term in the equation. The coefficient "c" is 1, meaning the y-intercept of the function is (0,1).

3. Analyze the vertex: The vertex of a quadratic function can be determined using the formula x = -b / (2a). In this case, b = 0 and a = -1. Therefore, the vertex is located at (0, 1).

4. Determine the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. In this case, the axis of symmetry is the line x = 0 (or the y-axis).

5. Sketch the graph: Using the information about the vertex and the axis of symmetry, you can plot the graph of the function. Since the coefficient "a" is negative, the parabola will open downwards.

6. Find the y-intercept: The y-intercept is the value of y when x is equal to 0. In this equation, the y-intercept is (0, 1).

7. Determine the x-intercepts: To find the x-intercepts, set y equal to zero in the equation and solve for x. In this case, you have -x^2 + 1 = 0. By solving the equation, you can find the x-intercepts.

By following these steps and practicing similar problems, you will become more comfortable with analyzing and graphing quadratic functions.