for this one x is -3 to 3 and values for y = x squared + 2x + 1 solve this quantivtive graph

To solve this quantitatively and construct the graph of the quadratic function \( y = x^2 + 2x + 1 \), we first need to calculate the values of \( y \) for various values of \( x \) in the range from \( -3 \) to \( 3 \).

### Step-by-Step Calculation of \( y \) Values:
1. **When \( x = -3 \)**:
   \[
   y = (-3)^2 + 2(-3) + 1 = 9 - 6 + 1 = 4
   \]
2. **When \( x = -2 \)**:
   \[
   y = (-2)^2 + 2(-2) + 1 = 4 - 4 + 1 = 1
   \]
3. **When \( x = -1 \)**:
   \[
   y = (-1)^2 + 2(-1) + 1 = 1 - 2 + 1 = 0
   \]
4. **When \( x = 0 \)**:
   \[
   y = (0)^2 + 2(0) + 1 = 1
   \]
5. **When \( x = 1 \)**:
   \[
   y = (1)^2 + 2(1) + 1 = 1 + 2 + 1 = 4
   \]
6

Solve the quadratic equation y = x^2 + 2x + 1 and graph it for values of x ranging from -3 to 3. This problem provides step-by-step calculations of the y-values and explores key concepts of quadratic functions. Ideal for students in Grades 7-9.

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