Question

Esmeralda is graphing a polynomial function as a parabola. Before she begins graphing it, explain how to find the vertex. Make sure you include how to determine if it will be a maximum or minimum point. Use an example quadratic function to help you explain and provide its graph.

Answer 1

Ok, so finding the vertex is easy in vertex form, but if she's in standard form Esmie needs to complete the square

Answer 2

So, once Esmers has done that, she'll have an equation of the form \[a(x-h)^2+k\]

Answer 3

So, what her h value is ( she needs to be careful of the subtraction sign in front of it) and her k value is the vertex. The vertex is (h,k)

Answer 4

Now the a value should not be ignored, if its positive it opens up and has a minimum, if negative, it does the opposite