solve y greater than equal to x squared minus 4 - Quadratic Inequalities VERY IMPORTANT In ALGEBRA!

[@stevendebettencourt7651]

Oh, this has a great point on further analysis. Thank you Mr. KZbin Math Man. y >= x^2 - 4 Let’s take a look at the graph of equality for these two. y = x^2 - 4 As a quadratic equation, the graph will be a parabola that has reflective symmetry along the x=-line that its apex passes through. I won’t go into detail of how to find this (Hint: Simple Calculus), but I trust you know what this should look like. Note that the leading coefficient of x^2 is 1. That means our parabola goes off to infinity in graph quadrants 1 and 2 (the top half) and has “average” steepness. Now that we have our parabola shape, we need to know where to put it. We’ll start easy: the y-intercept: x = 0; y = (0)^2 -4 y = 0 - 4 y = -4 So the point (0,-4) is on the parabola. Now the roots. y = x^2 - 4 = 0 x = -(0) +- GOTCHA! Of course I know the difference of two squares when I see them. (x + 2)(x - 2) = 0 x + 2 = 0 OR x - 2 = 0 x = -2 OR x = 2 We can also add (-2,0) and (2,0) to (0,-4) as points on this parabola. These three points can actually completely define the entire parabola, assuming we know it IS a parabola. Finally, remember that: y >= x^2 - 4 So the line itself will be part of our graph, but we also include all values for which y is greater than x^2 - 4. These are all the points “inside the arms” of our parabola, so to speak. This area should be shaded in. Now, further analysis. Let’s set y=5 and solve: y = 5 >= x^2 - 4 9 >= x^2 Now, here’s where it gets tricky. Take the square root of both sides: Sqrt(9) >= sqrt(x^2) Now, on the left, the square root of 9 is 3. Not -3, not +-3. The square root of a number is its principle square root. On the right, sqrt(x^2) is defined as |x|. Thus: 3 >= |x| Now we split the absolute value. x

[@tomtke7351]

wow... 1) "y>=" means everything residing above the equation. I.E. plot y=x^2-4 and shade the entire area from it & above it. 2) the x^2 function is an upward facing parabola mirrored about the y=0 axis. 3) its minimum is y=-4 which occurs at x=0.

[@TO-ps2qq]

I used to be able to do this.

[@raya.pawley3563]

Thank you

[@paulfrank8738]

Being nit-picky, but the problem is already solved. It took me a minute to realize that you probably wanted a graph of the equation. Nit-pickiness aside, your videos are great. Thanks for doing them.

[@russelllomando8460]

thanks for the fun

[@helenaamaral4659]

It's a interval {2,+§}

[@helenaamaral4659]

It's a function.

[@helenaamaral4659]

Its a function. I was wrong.

[@thomasharding1838]

EASY!! X can equal 1 and Y can equal 392,456. 392, 456 is equal to or greater than 1 squared - 3.

[@jameshohimer2542]

Why not just make a standard X, Y, table of values(if X is _ then Y=_) to draw the curve? No need for all that extra stuff!

[@Bill91190]

Y=12 X=4 I had that figured out on paper in 30 seconds. That was the problem you asked me to solve. Then you added a graph. That graph changes the problem. Fk your graph problem. I answered the original problem correctly. I demand my A on the first problem you presented. 😅