Find the intercepts and graph the equation by plotting points.
yequalsx squared minus 4
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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.)

To find the intercepts of the equation \( y = x^2 - 4 \), we need to determine where the graph crosses the x-axis and the y-axis.

### **X-intercepts:**
X-intercepts occur where \( y = 0 \). So, set \( y = 0 \) and solve for \( x \):

\[
0 = x^2 - 4
\]

This simplifies to:

\[
x^2 = 4
\]

Taking the square root of both sides:

\[
x = \pm 2
\]

Thus, the x-intercepts are at \( (2, 0) \) and \( (-2, 0) \).

### **Y-intercept:**
The y-intercept occurs where \( x = 0 \). Plug \( x = 0 \) into the equation:

\[
y = 0^2 - 4 = -4
\]

Thus, the y-intercept is at \( (0, -4) \).

### **Intercepts:**
- X-intercepts: \( (2, 0) \) and \( (-2, 0) \)
- Y-intercept: \( (0, -4) \)

Would you like to see the graph, or do you have any questions about the solution?

Here are 5 questions to expand your understanding:
1. How would the graph change if the equation was \( y = x^2 + 4 \)?
2. What would the intercepts be if the equation was \( y = x^2 - 9 \)?
3. What is the vertex of the parabola represented by \( y = x^2 - 4 \)?
4. How do the intercepts relate to the symmetry of the parabola?
5. Can you find the axis of symmetry for the parabola?

**Tip:** When solving for x-intercepts, always remember to set \( y = 0 \) and solve for \( x \).

Find the intercepts and graph the equation by plotting points. y equals x squared minus 4. What are the intercepts? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Discover how to find the intercepts of the quadratic equation y = x^2 - 4 and graph it by plotting points. This guide walks through identifying x-intercepts and y-intercepts, using essential algebraic concepts and graphing techniques. Ideal for students in Grades 8-10.

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