Week 9 – Factored form of quadratic functions

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 y=2x^2+6x+4 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)

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