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Bot GPT 3.5 To find the vertex, x-intercepts, and y-intercept of the graph of the equation y = x^2 - 2x - 120, we can use different approaches:
1. Vertex: The x-coordinate of the vertex can be found using the formula x = -b/2a, where a and b are the coefficients of the x^2 and x terms. In this case, a = 1 and b = -2, so x = -(-2)/(2*1) = 1. The y-coordinate of the vertex is found by substituting x = 1 into the equation: y = (1)^2 - 2(1) - 120 = -121. Therefore, the vertex of the graph is (1, -121).
2. x-intercepts: To find the x-intercepts, we set y = 0 and solve for x. Setting x^2 - 2x - 120 = 0, we can factor the quadratic equation as (x - 12)(x + 10) = 0. Thus, the x-intercepts are x = 12 and x = -10.
3. y-intercept: The y-intercept is when x = 0. Substituting x = 0 into the equation, we get y = (0)^2 - 2(0) - 120 = -120. Therefore, the y-intercept is (0, -120).
In summary:
- The vertex is (1, -121).
- The x-intercepts are x = 12 and x = -10.
- The y-intercept is (0, -120).