What are the key points on the graph of y=x2−2x−120
? Name the vertex, x-intercepts, and y-intercept.
Make sure your answer has is written in coordinate form ( _ , _ ).
The given equation is y = x^2 - 2x - 120.
To find the vertex, use the formula x = -b / (2a). In this case, a = 1 and b = -2.
x = -(-2) / (2 * 1) = 1
To find the y-coordinate of the vertex, substitute the value of x back into the equation:
y = (1)^2 - 2(1) - 120 = 1 - 2 - 120 = -121
Therefore, the vertex is (1, -121).
To find the x-intercepts, set y = 0 and solve for x:
0 = x^2 - 2x - 120
Factorizing this equation:
0 = (x + 10)(x - 12)
Setting each factor equal to zero:
x + 10 = 0 or x - 12 = 0
x = -10 or x = 12
Therefore, the x-intercepts are (-10, 0) and (12, 0).
To find the y-intercept, set x = 0:
y = (0)^2 - 2(0) - 120 = 0 - 0 - 120 = -120
Therefore, the y-intercept is (0, -120).
The key points on the graph of y = x^2 - 2x - 120 are:
- Vertex: (1, -121)
- x-intercepts: (-10, 0), (12, 0)
- y-intercept: (0, -120)