How do you find the x-intercepts of the curve $y = x^2 - 4$?

Conditions

• The curve is defined by the quadratic equation $y = x^2 - 4$.
• The goal is to find where the graph crosses the x-axis.
• The algebraic method used is factoring the difference of perfect squares.

Reasoning, step by step

1. Set the y-value of the function to zero: $x^2 - 4 = 0$.
2. Recognize the expression $x^2 - 4$ as a difference of squares.
3. Factor the equation: $(x+2)(x-2) = 0$.
4. Apply the zero-product property by setting each factor to zero.
5. Solve for x to find the intercepts: $x = -2$ and $x = 2$.

Example

The video states: "Now what I'm going to do is find the x-intercepts. So if we set the function equal to zero... We can factor it using the difference of perfect squares technique... we're going to get x equals two and x is equal to negative two."

Common misconceptions

• Forgetting to set the function equal to zero before solving.
• Attempting to take the square root of both sides without considering the negative root (i.e., missing $x = -2$).
• Confusing x-intercepts with y-intercepts.

Watch the explanation

Explore next

• How is the graph of $y = x^2 - 4$ related to the graph of $y = x^2$?
• How do you find the y-coordinate of a point on the curve for a given x-value?
• What is the difference of squares factoring formula?