What are the key points on the graph of y=x2−2x−120%0D%0A%0D%0A=%0D%0A%0D%0A2%0D%0A−%0D%0A2%0D%0A%0D%0A−%0D%0A120%0D%0A ? Name the vertex, x-intercept(s), and y-intercept.
To find the key points on the graph of y = x^2 - 2x - 120, we need to determine the vertex, x-intercepts, and y-intercept.
1. Vertex:
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a is the coefficient of the x^2 term and b is the coefficient of the x term. In this case, a = 1 and b = -2, so the x-coordinate of the vertex is:
x = -(-2) / (2*1) = 2/2 = 1
To find the y-coordinate of the vertex, substitute the x-coordinate back into the equation:
y = (1)^2 - 2(1) - 120
y = 1 - 2 - 120
y = -121
Therefore, the vertex of the parabola is (1, -121).
2. X-intercepts:
To find the x-intercepts, set y = 0 and solve for x:
x^2 - 2x - 120 = 0
This quadratic equation can be factored as:
(x - 12)(x + 10) = 0
Setting each factor equal to zero:
x - 12 = 0 --> x = 12
x + 10 = 0 --> x = -10
Therefore, the x-intercepts of the graph are x = 12 and x = -10.
3. Y-intercept:
To find the y-intercept, set x = 0 and solve for y:
y = (0)^2 - 2(0) - 120
y = -120
Therefore, the y-intercept of the graph is at y = -120.
In summary:
- Vertex: (1, -121)
- X-intercepts: x = 12 and x = -10
- Y-intercept: y = -120