What are the key points on the graph of y=x^2−2x−120 ? Name the vertex, x-intercepts, and y-intercept. Make sure your answer has is written in coordinate form ( _ , _ ). (3 points) The vertex is: . The x-intercept(s) are: . The y - intercepts is:
The given equation is y = x^2 - 2x - 120.
To find the vertex, we can use the formula x = -b/2a. In the given equation, a = 1, and b = -2. Therefore,
x = -(-2)/(2*1) = 2/2 = 1.
To find the y-coordinate of the vertex, substitute x = 1 into the equation:
y = 1^2 - 2(1) - 120
= 1 - 2 - 120
= -121.
Thus, the vertex is (1, -121).
To find the x-intercepts, set y = 0 and solve for x:
0 = x^2 - 2x - 120.
This equation can be factored as:
0 = (x - 12)(x + 10).
Setting each factor equal to zero, we find:
x - 12 = 0 ---> x = 12,
x + 10 = 0 ---> x = -10.
Therefore, the x-intercepts are (12, 0) and (-10, 0).
To find the y-intercept, set x = 0 and solve for y:
y = (0)^2 - 2(0) - 120
= 0 - 0 - 120
= -120.
Thus, the y-intercept is (0, -120).
Therefore, the key points on the graph are:
The vertex is (1, -121).
The x-intercepts are (12, 0) and (-10, 0).
The y-intercept is (0, -120).