Question

I need help with quadratic functions

I need to know how to identify

1 y intercepts
2 x intercepts
3 vertex
4 axis of symmetry
5 domain
6 range

This is the problem I need to graph and find all of those things for y=x^2+3x-18. I just need to learn how to do this so anyone can subsititute the problem for one they can do

Answer 1

to find the y intercepts, make x=0 and you get -18
find x intercepts, make y=0, since quadratic, you will get 2 values, symmetry you can see from graph
domain you can clearly see as there is no quotients or square roots all real numbers can go in, range all real numbers

Answer 2

there are other ways you can use along with the ones you listed, like finding the relative/absolute minima/maxima, find concavity.

the first derivative of the quadratic function is y'=2x+3, the derivative can clearly tell you where the graph is going up or down and where its horizontal, if you make y'=0, then at x=-3/2 the graph is horizontal, if you plug in x values before or after that you get how it looks, lets put y'(0)=2(0)+3, -> y'(0)=3 so at x=0 slope is 3, in otherwords, it is increasing, you try yourself plugging value before -3/2

what you saw before is consistent with second derivative test, the second derivative test tells you the concavity of the graph, wether its open up or down, or both and where are the points where they turn

y''=2, its positive, so it means that the graph is concave upwards, like a u shape

Answer 3

i recommend you read the book, "Thomas Calulus", chapter 4.1-4.4