Find the intercepts and graph the equation by plotting points.

yequals=negative x squared plus 1−x2+1

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Part 1

What are the​ intercepts? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. 

A.

The​ intercept(s) is/are 

enter your response here.

​(Use a comma to separate answers as needed. Type an ordered​ pair.)

B.

There are no intercepts. and show me what it looks like on the chart

Here is the graph of the equation \( y = -x^2 + 1 \). 

### **Intercepts:**
- **X-Intercepts:** \((1, 0)\) and \((-1, 0)\)
- **Y-Intercept:** \((0, 1)\)

The curve is a downward-opening parabola, as shown on the graph, passing through the intercepts.

### Do you have any questions or need further details? Here are 5 related questions to consider:

1. How do you find the vertex of a parabola from its equation?
2. What is the significance of the parabola's orientation (upward vs. downward)?
3. How can you determine the axis of symmetry for a parabola?
4. What effect does changing the coefficient of \(x^2\) have on the graph of a parabola?
5. How can you graph a parabola using its vertex and intercepts?

**Tip:** Always check the signs of the coefficients in a quadratic equation to understand how the graph will open (upward or downward).

Learn how to graph the quadratic equation -y = x^2 + 1 with step-by-step instructions and interpret the intercepts. This problem explores the concepts of quadratic equations and graphing in high school mathematics.

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