Determine which of the following is a graph of y= x squared + 1 by plotting at least 3 points 

To determine the graph of the equation \( y = x^2 + 1 \), we can plot a few key points by substituting values for \( x \):

1. **When \( x = -2 \)**:
   \[
   y = (-2)^2 + 1 = 4 + 1 = 5 \quad \Rightarrow \quad (-2, 5)
   \]

2. **When \( x = -1 \)**:
   \[
   y = (-1)^2 + 1 = 1 + 1 = 2 \quad \Rightarrow \quad (-1, 2)
   \]

3. **When \( x = 0 \)**:
   \[
   y = 0^2 + 1 = 0 + 1 = 1 \quad \Rightarrow \quad (0, 1)
   \]

4. **When \( x = 1 \)**:
   \[
   y = 1^2 + 1 = 1 + 1 = 2 \quad \Rightarrow \quad (1, 2)
   \]

5. **When \( x = 2 \)**:
   \[
   y = 2^2 + 1 = 4 + 1 = 5 \quad \Rightarrow \quad (2, 5)
   \]

### Points to Plot
The points we have are:
- \( (-2, 5) \)
- \( (-1, 2) \)
- \( (0, 1) \)
- \( (1, 2) \)
- \( (2, 5) \)

### Sketching the Graph
Plotting these points on a Cartesian plane, we can see that the shape of the graph forms a parabola that opens upwards. The vertex of the parabola is at the point \( (0, 1) \).

### Summary
The graph of \( y = x^2 + 1 \) is a parabola with its vertex at \( (0, 1) \) and symmetrical around the y-axis.

Do you want more details or have any questions? Here are some related questions you might consider:

1. What are the properties of the graph of a quadratic function?
2. How do you find the vertex of a parabola from its equation?
3. What transformations can occur with the equation \( y = x^2 + k \)?
4. How would the graph change if the equation were \( y = x^2 - 3 \)?
5. Can you explain the concept of the axis of symmetry in relation to parabolas?

**Tip:** Remember that the vertex form of a quadratic equation is \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex.

Determine which of the following is a graph of y = x squared + 1 by plotting at least 3 points.

Discover how to graph the equation y = x^2 + 1 by plotting key points. This guide illustrates important points such as (-2, 5), (-1, 2), (0, 1), (1, 2), and (2, 5), highlighting the properties of the parabola. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation