To find the key points on the graph of the quadratic function y=x^2-2x-120, we can start by identifying the vertex, x-intercepts, and y-intercept.
1. Vertex:
The vertex of a quadratic function in the form of y=ax^2+bx+c is given by the coordinates (-b/2a, f(-b/2a)). For our function, a=1, b=-2, and c=-120. Thus, the x-coordinate of the vertex is -(-2)/(2(1)) = 1, and the corresponding y-coordinate is f(1) = 1^2 - 2(1) - 120 = -121. Therefore, the vertex is (1, -121).
2. X-intercepts:
To find the x-intercepts, we need to solve the quadratic equation x^2 - 2x - 120 = 0. This can be factored as (x - 12)(x + 10) = 0. Setting each factor equal to zero, we have x - 12 = 0, yielding x = 12, and x + 10 = 0, giving x = -10. Therefore, there are two x-intercepts at (12, 0) and (-10, 0).
3. Y-intercept:
The y-intercept occurs when x is equal to zero. Substituting x = 0 into the equation y = x^2 - 2x - 120, we find y = 0^2 - 2(0) - 120 = -120. Hence, the y-intercept is (0, -120).
In summary, the key points on the graph of the function y = x^2 - 2x - 120 are:
- Vertex: (1, -121)
- X-intercepts: (12, 0) and (-10, 0)
- Y-intercept: (0, -120)
What are the key points on the graph of y=x^2-2x-120? Name the vertex, x-intercepts, and y-intercepts.
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