This week in Math we learned how to interperet graphs of quadratic functions in the form a(x-x1)(x-x2).
Ex. We can convert the general form of into factored form.
y=2(x+2)(x+1)
We can now find the x intercepts by utilizing the zero product law.
0=2(x+2)(x+1)
x=-2,-1
If we now plot these points on the graph, we can determine the axis of symmetry by figuring out the x value in the middle of these points, in this case, the AOS would be x=-1.5. We now also have the first x value of our vertex. We can then plug in this x value into our equation to solve for y value of the vertex.
y=2(-1.5+2)(-1.5+1)
y=-0.5
Vertex:(-1.5,-0.5)