Graph the function y, equals, x, squared, plus, 3y=x 
2
 +3 using the given table of values and following the instructions below.
xx	yy
minus, 10−10	103103
minus, 9−9	8484
minus, 8−8	6767
minus, 7−7	5252
minus, 6−6	3939
minus, 5−5	2828
minus, 4−4	1919
xx	yy
minus, 3−3	1212
minus, 2−2	77
minus, 1−1	44
00	33
11	44
22	77
33	1212
xx	yy
44	1919
55	2828
66	3939
77	5252
88	6767
99	8484
1010	103103
Plot at least five points from the table of values on the axes below. Click a point to delete it.
x
y
Answer
Attempt 1 out of 2
You must answer all questions above in order to submit.

Let's graph the function given the table of values. The function provided, which appears to be \( y = x^2 + 3 \), has the corresponding table of values:

**Table of Values**:

| \( x \) | \( y \) |
|---------|---------|
| -10     | 103     |
| -9      | 84      |
| -8      | 67      |
| -7      | 52      |
| -6      | 39      |
| -5      | 28      |
| -4      | 19      |
| -3      | 12      |
| -2      | 7       |
| -1      | 4       |
| 0       | 3       |
| 1       | 4       |
| 2       | 7       |
| 3       | 12      |
| 4       | 19      |
| 5       | 28      |
| 6       | 39      |
| 7       | 52      |
| 8       | 67      |
| 9       | 84      |
| 10      | 103     |

To plot at least five points from this table, you can select five values of \( (x, y) \). Here are some recommended points to plot:

1. \( (-5, 28) \)
2. \( (-3, 12) \)
3. \( (0, 3) \)
4. \( (3, 12) \)
5. \( (5, 28) \)

**Plotting the Points**:
1. Start by marking the x-axis and y-axis on the graph.
2. Plot the points \( (-5, 28) \), \( (-3, 12) \), \( (0, 3) \), \( (3, 12) \), and \( (5, 28) \) on the graph. 
3. Connect these points smoothly to form the parabolic shape of the function \( y = x^2 + 3 \).

**Graph Characteristics**:
- The graph is a parabola opening upwards, shifted 3 units up from the standard position of \( y = x^2 \).

Would you like a detailed graph of this function, or do you have any specific questions about plotting these points? 

### Follow-Up Questions:
1. What happens to the graph if you change the constant value in the function?
2. How would the graph look if the function were \( y = -x^2 + 3 \)?
3. What is the vertex of the parabola represented by this function?
4. How does changing the coefficient of \( x^2 \) affect the width of the parabola?
5. How can you determine the symmetry of the graph based on its function?

### Tip:
To quickly identify key points on a parabola, always start with the vertex and symmetry points around it!

Graph the function y = x^2 + 3 using the given table of values and following the instructions below.

Learn how to graph the quadratic function y = x^2 + 3 using a table of values. This solution demonstrates how to plot key points and identify the parabolic shape of the function. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation