Question

y = x^2 − 2x − 3

Find the vertex.
Find the x-intercepts.
Describe the graph.

Answer 1

Let's see...for the vertex "-b/2a" so that's 2/2(1) = 1 (Vertex)

Answer 2

the vertex is at the point where the derivative or slope of this function is zero
so dy/dx=2x-2
2x-2=0
x=1
so substituting in f(x) we get 1-2-3=-4
so vertex at (1,-4)
as the function is in x and the coefficient of x is positive the graph is like

Answer 3

we get x intercept when the graph touches x axis so putting y=0 in the function we get x^2-2x-3=0 now solve the quadratic equation to get the x intercept