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The given equation is \( y = x^2 - 4 \), and you are asked to graph it for integer values of \( x \) from \(-3\) to \(3\), inclusive.

Let's first compute the corresponding \( y \)-values for each \( x \)-value in that range:

- For \( x = -3 \): 
  \[
  y = (-3)^2 - 4 = 9 - 4 = 5
  \]
- For \( x = -2 \):
  \[
  y = (-2)^2 - 4 = 4 - 4 = 0
  \]
- For \( x = -1 \):
  \[
  y = (-1)^2 - 4 = 1 - 4 = -3
  \]
- For \( x = 0 \):
  \[
  y = 0^2 - 4 = 0 - 4 = -4
  \]
- For \( x = 1 \):
  \[
  y = 1^2 - 4 = 1 - 4 = -3
  \]
- For \( x = 2 \):
  \[
  y = 2^2 - 4 = 4 - 4 = 0
  \]
- For \( x = 3 \):
  \[
  y = 3^2 - 4 = 9 - 4 = 5
  \]

Now that we have the points \((-3, 5)\), \((-2, 0)\), \((-1, -3)\), \((0, -4)\), \((1, -3)\), \((2, 0)\), and \((3, 5)\), we can plot these on a graph. The shape of the graph will be a parabola, as this is a quadratic equation.

Would you like me to provide the graph as well?

### Expanding the concept:

1. What is the general shape of a quadratic function like \( y = x^2 - 4 \)?
2. How would the graph change if the equation were \( y = -x^2 - 4 \)?
3. What is the vertex of the parabola for the equation \( y = x^2 - 4 \)?
4. How does the value of \( -4 \) in \( x^2 - 4 \) affect the graph's position?
5. What happens to the graph if we change the equation to \( y = (x - 1)^2 - 4 \)?

#### Tip: 
In a quadratic function \( y = ax^2 + bx + c \), the coefficient \( a \) controls the direction and width of the parabola, while \( c \) controls the vertical shift.

Graph the equation. Select integers for x from -3 to 3, inclusive. y = x^2 - 4

Learn how to graph the quadratic equation y = x^2 - 4 for integer values of x ranging from -3 to 3. This problem involves calculating corresponding y-values, understanding the properties of parabolas, and plotting points on a graph. Suitable for students in Grades 8-10.

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