In this video I want to solve the given equation
using the intersect method on the calculator. The first thing I’ll do is let the left side
be called y1, and the right side be called y2. Then if I look at the graphs of y1 and
y2, and see where those pictures cross or intersect, that gives me the x values where
the left side does equal the right side. In this case there are two points where those
curves intersect. I also can recognize that the square root graph is that first hook-shaped
curve, and a quadratic function, an x-squared function, always has the u-shaped graph. So
I see two points of intersection so I’m going to go through the process twice. The calculator
asks me a series of questions. It asks me “first curve” and “Second curve.”In our case,
those questions don’t really mean very much. Right now, I think I see the cursor blinking
down there, but let me use my right arrow to get it into view a little bit better – there
it is. So we can see it’s moving along my hook-shaped square root curve as I press my
left and right arrows. If I want, I can designate the parabola as the first curve. And I can
hop up to that curve using the up arrow. It really doesn’t make any difference which curve
you designate as the first curve or the second curve. The calculator is worried about the
case where you have three or four different curves on your screen and in that case it
would want you to pick two. Since we only have two curves we just pick our two curves!
So here’s my first curve, to pick it, I hit enter. Now notice my cursor jumped back down.
So for my second curve I hit enter. And now the calculator asks me to make a guess. It’s
going to start searching for a point where those two curves intersect, and it wants to
know about where should it start searching? So I use the left arrow to go over to where
I see that crossing, and I hit enter. Finally, the calculator announces “Intersection.”And
it tells me an x value. I get a y value for free, but it’s the x value that we’re interested
in. Looking back at the original problem, I can see I’m seeking a value of x that makes
these equal. So I just found one, x=2. That means those curves are in the same place at
the same time. I’m going to repeat the whole thing to find
that other intersection point. First curve, yes, first curve, yes, and this time for my
guess I’m going to move closer to this point. I’ll round to the nearest hundredth.

Radicals on the Calculator: Solving an equation with Intersect Method
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