SOLUTION: y=x^2 + 3*x I need to solve this complete the table and graph and find the roots, vertex and find 2 more points and find min and max. I don't know what to do

Question 281385: y=x^2 + 3*x
I need to solve this complete the table and graph and find the roots, vertex and find 2 more points and find min and max.
I don't know what to do
Found 2 solutions by richwmiller, Mathematicians:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
you said you don't know what to do not that you don't know how to do it.
so this is what you should do
complete the table
and graph
and find the roots, vertex and
find 2 more points and
find min and max.
Answer by Mathematicians(84) (Show Source): You can put this solution on YOUR website!
There are a couple ways you can go about solving this problem.
The roots is basically finding when y = 0.
So your equation can be written as
Also remember factoring

or
Both roots are:

Finding the vertex, min or max is nearly the same process so I'll find two additional points. To find two additional points, pick out any two x values you want. Lets say x = -2 and x = -1. We need to find the y values so:

one point is (-2,-2)
another point is (-1,-2)
Finally the vertex and min or max. Since this is a parabola which is a U shape graph, you are either going to have a minimum or a maximum that is not infinite. We can tell your parabola opens upward because the coefficient near the is a positive number. It so happens at the vertex will be either a maximum or a minimum and in our case, it will be a minimum (because it will be the lowest point). We can use the vertex formula:
If (h,k) is your vertex, then:

where you have a quadratic equation
In our case, , we can find our k by plugging in -3/2 into our equation:

Which implies (-3/2,-9/4) is the vertex and with our last statement is a minimum.
Hopes this helps!
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