Solve Quadratic Inequalitesby Graphing - Example 2
Solve Quadratic Inequalitesby Graphing - Example 3
Solve Quadratic Inequalitesby Graphing - Example 4
Adding Subtractingand Multiplying Complex Numbers
Complexand Imaginary Numbers
Liberty University
Solve Quadratic Inequalitesby Graphing - Example 1


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quadratic inequality to solve it. And we're going to do so by the quadratic formula. Quadratic formula says that negative B plus or minus the square root of B squared minus four A. C over two A. So let's plug our numbers in. So I mean X is gonna equal negative negative seven plus or minus the square root of negative seven squared minus four times, three times negative, one over two times three. So when I simplify that, I'm gonna have positive seven plus or minus square root off 49 plus 12 over six, which would reduce to seven plus or minus the square root of 61 over six. Now, 61 is not a perfect square, so it is a complex number. So we're going, and actually we're gonna leave it like this, so we're gonna have two possible solutions. So one would be X would equal seven plus the square to 61/6, which would be approximately 2.47 We're gonna use those numbers women graph and X would equal seven minus the square root of 61/6, which would be approximately 0.9. So we're gonna use the 2.47 I'm sorry, not 0.9 negative. 0.14 So we're gonna use those two numbers in our graph, so we're gonna have X can be 2.47 and negative 0.14 And these were both where why equals zero. So we're going to kind of go ahead and graph those. So these we're gonna kind of be an estimate to kind of see and for these? That's actually okay, So that would be about the 2.47 It'll be about between the two and three. Negative 0.14 to be about right there. It actually be a little bit closer to the zero. But we can kind of get the idea for this purpose. Um, just to kind of draw a graph in a few things, this is a positive. So this is gonna be an open parabola. We can go ahead our y intercept if we want to. Kind of get a little bit more exact. Graph is going to be negative one. So it would be right there and our axis of symmetry would be negative. Seven over two times three is six. So negative 7/6. So it's gonna be between those points right there. So to kind of get your idea is gonna look somewhat similar to this right here. It's not exact, but what we're looking for, really, where those points are now. The other thing we gotta look for is we are looking at one that says it is less than or equal to zero. In this case, our vertex falls below the X axis, which means it's less than zero. So when I'm writing my solution, this is a compound because it says less than this is gonna be compound. So we're gonna say that negative 0.14 is less than or equal toe eggs, which is less than or equal to 2.4 seven.

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