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Bot GPT 3.5 To find the x-intercepts, we need to set y = 0 and solve for x.
Setting y = 0:
x^2 + 3x + 8 = 0
Unfortunately, this quadratic equation does not factor easily. We can solve for the x-intercepts by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
For this equation, a = 1, b = 3, and c = 8:
x = (-3 ± √(3^2 - 4(1)(8))) / 2(1)
x = (-3 ± √(9 - 32)) / 2
x = (-3 ± √(-23)) / 2
Since the discriminant (b^2 - 4ac) is negative, the equation has no real solutions. Therefore, there are no x-intercepts for the graph of y = x^2 + 3x + 8.