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

Поділитися
Вставка
  • Опубліковано 23 гру 2024

КОМЕНТАРІ • 12

  • @stevendebettencourt7651
    @stevendebettencourt7651 День тому +1

    Oh, this has a great point on further analysis. Thank you Mr. UA-cam 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
    @tomtke7351 День тому +1

    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
    @TO-ps2qq День тому +1

    I used to be able to do this.

  • @raya.pawley3563
    @raya.pawley3563 День тому

    Thank you

  • @paulfrank8738
    @paulfrank8738 День тому

    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
    @russelllomando8460 День тому

    thanks for the fun

  • @helenaamaral4659
    @helenaamaral4659 День тому

    It's a interval {2,+§}

  • @thomasharding1838
    @thomasharding1838 День тому

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

  • @jameshohimer2542
    @jameshohimer2542 День тому

    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
    @Bill91190 День тому

    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. 😅