How many x-intercepts does the graph of the equation y = x^2 – 12 have?

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To determine the number of x-intercepts for the graph of the equation y = x2 – 12, we need to find the values of x where y equals zero. This means we set the equation as follows:

0 = x2 – 12

Next, we can rearrange the equation to solve for x:

x2 = 12

Now, we take the square root of both sides. Remember that taking the square root will yield both a positive and a negative solution:

x = ±√12

Thus, we find:

  • x = √12
  • x = -√12

Since both of these solutions are real numbers, we conclude that the graph of the equation has two x-intercepts. These intercepts occur at the points (√12, 0) and (-√12, 0).

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