This week in Precalc 11, I learned about parabolic inequalities. It’s very similar to my last post about linear inequalities but this time, instead of being a linear line, it will be a parabola and we will be using vertex form.
Let’s get started.
In my last post I explained the different meanings of each symbol and those will apply here as well. I will quickly explain that the area shaded is where the solution of y can be. So if y is bigger than an equation, then the shaded area will be above the line. Another way to figure out if the area you shaded is correct is by taking a coordinate and placing it into the equation, if the equation is true then the area that you shaded is correct.
So first let’s start with an equation
y>(x-2)^2+2
When we put this into desmos we get this…
We can see that our line is dotted since y does not include the coordinates of the parabola. We can also see that the shaded area matches up with our equation since the value of y is bigger than the coordinates of the parabola. We can double check by taking a coordinate from inside the shaded area and putting it into the equation. Let’s use (2,6)
6>(2-2)^2+2. We end up with 6>2 which is true so that means our shaded area is correct.
The same rules will apply to the less than (<) equations as seen below. We can double check by using the coordinates (0,0) since it is in our shaded area.
0<(0-2)^2+2. We end up with 0<6 which is true so our shaded area is correct.
The same rules apply for this but the line is solid since our symbol is including the coordinates of the parabola.
