00:01
All right, in this problem, we need to decide whether this function right here has a maximum or a minimum and how we know.
00:11
Okay, so right away, i noticed that our coefficient on the x squared term is 2.
00:18
That is a positive number.
00:20
And we talked about in the last problem, how if a, so in our general form, y equals a x squared plus bx plus a.
00:31
See if this a is positive, then we think it is going to open up kind of like that, smiley face with the 2 plus sign eyes.
00:41
Okay, so let's test that theory by graphing it or substituting some values and seeing what it looks like on the graph.
00:48
Okay, so starting with negative 5, if this is our x value, we can substitute that every time we see an x.
00:56
Okay, so starting with y equals two, and instead of x, we're going to substitute to do that negative 5 squared plus 12 and then instead of that x negative 5 plus 11 okay and we can note that this is negative 5 squared is 25 times 2 so 50 and then negative 12 times 5 is 60 but this is going to be a negative 60 so negative 50 plus 60 plus 11 okay so this gets us a total of 50 is 1.
01:39
So we know that the very first point on our graph is gonna be negative 5 comma.
01:46
Okay, continuing on this exact same way...
