Solving Quadratic Equationsby Completingthe Square - Example 3
The Discriminant - Example 3
Adding Subtracting And Multiplying Complex Numbers - Example 4
Complexand Imaginary Numbers - Example 4
Dividing Complex Numbers - Example 4
Liberty University
Solve Quadratic Equationsby Graphing - Example 3


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Agent X Square minus non X equals negative 18. Now in order. The first thing we're gonna do is we're gonna have to make this quadratic equation equals zero. So we're gonna do that by adding 18 to both sides. So that means I'll have X squared minus non X plus 18 will equal zero. The next thing we're gonna do is we're gonna find our y intercept or why intercept is where it crosses the Y axis. Well, in this case, our Y intercept is going to be 18. So where? X zero. Why is gonna be 18? So that's gonna be pretty high up. I'm actually not gonna be putting that point on the graph because I don't have enough space. But that's just gonna kind of let you know we're gonna be using some different numbers on this one. Let's also go ahead and find the axis of symmetry so they can kind of tell me at what point do we need thio numbers? Can we look for X? So we know the axis of symmetry to find it is negative, be over to a so in this case will have negative negative nine over two times one, which would be positive nine over to, and that's the same as 4.5 or 4.5. So that means and it's positive. So So that means my axis of symmetry is going to be somewhere around here. So this is where the Vertex would be as far as the X of the Vertex. So we need to kind of work from this point out. So that means to the left of the axis of symmetry, my lines are gonna be going one direction to the right of that access is gonna be going opposite. Well, since my axis of symmetry is 4.5, let's start with four and five because forced to the left that fives to the right and let's start with their as my first two points. So that would be four squared minus non times four plus 18. And that would be 16, minus 36 plus 18. And that's going to give me negative to so we would have negative two at four. So now let's do five so we'd have five squared minus nine. Tom's five plus eighteens. That'd be 25 minus 45 plus 18 would also equal negative, too. So somewhere between four and five is where I would have my Vertex. So let's keep going. So the left, let's try three. And then we would do six, so we'd have picked a different color. Let's do three squared minus nine times three plus 18. So that would be nine minus 27 plus 18, which would give me zero. So that tells me that three is going to be one of my points, my solutions. And then let's do six. So we have six squared minus nine times six plus 18. So that would be 36 minus 54 plus 18 would also give me zero. So now, even though I don't know all my points, I can kind of sell the direction my parabolas going. And so I can also see my solution. And I can see my two points that it crosses the X axis. That what? So that means that X equals three and X equal six. And if you wanted to check, you could put these both into the equation like we did in place of eggs and make sure they give you zero for a while.