Answer:
Vertex: (50, -100)
X-intercepts: (40, 0), (60, 0)
Y-intercept: (0,2400)
What is vertex-form?
For a parabolic equation, written in y = a(x-h) +k format, it is in vertex form. This is because we can derive the vertex just by looking at the equation; and from this the vertex is (h, k). In our equation, h is 50, and y is -100, so our vertex is (50, -100).
What is the x-intercept?
The x-intercept value of a function is the value of x when y is zero. It is a dot on the x-axis. We can use this by plugging it into the equation.
0 = (x-50)^2 -100
100 = (x-50)^2
+/- 10 = x -50
X = 40, x = 60
So our two x-intercepts will be (40,0) and (60,0)
What is the y-intercept?
Like the x-intercept, it is the y-value of a function when the x-value is zero. We can plug this in:
y = (0-50)^2 -100
Y = 2500 - 100
Y = 2400
So our y-intercept is (0,2400)
Vertex: (50, -100)
X-intercepts: (40, 0), (60, 0)
Y-intercept: (0,2400)