Graph the equation y − x 2 + 3 = 0 y-x^2+3=0 y − x 2 + 3 = 0 by choosing points that satisfy the equation .

Welcome back, everyone. So in this problem, we're gonna graph this equation y minus x squared plus 3 equals 0. And because we're not given any x points in our table, we're gonna have to choose some that satisfy the equation. Alright? So let's get started. The first step to graphing by plotting a bunch of points is to isolate y to the left side of the equation. You want y by itself so that you can plug a bunch of x values in and get your y values. Alright? So I'm gonna have to take this equation and isolate, y. So I'm gonna have to move the x squared over, and that's gonna be plus x squared. I'm gonna have to move the positive 3 over, and that becomes a minus 3. So what I'm left with over here is these cancel, and is I'm left with y equals x squared minus 3. Alright? So this is my equation for y, and I'm done with the first step. And now what I'm gonna do is I'm gonna calculate a bunch of y values from 3 to 5 chosen x values. And, again, because they're not given to us, we're just gonna have to pick some. If you're ever unsure of which, you know, which numbers to pick, always try to pick low numbers because the higher numbers are just gonna be more tedious sort of hard calculations. So I always like to pick low numbers. And in this case, what I'm gonna do is I'm just gonna pick 0, 1, 2, and then also negative one and negative 2. So some negative numbers and positive numbers so I can see what the general shape of this graph is for those low values. Alright. So let's get started here. Now the easiest one to actually plug in is gonna be 0 because what happens is when you have y equals and then you plug in 0 in for x, this whole term actually just goes away, 0 squared 0. So 0 minus 3 just equals negative 3, and that's gonna be your y value. So the coordinate, the ordered pair for this particular point is 0 comma negative 3. Alright? Now we're gonna plot them later on. Let's just do all the calculations first. So let's go over to 1 because one is also a pretty number easy number to calculate. So I've got y equals 1 squared minus 3. This is actually just 1 minus 3, which is negative 2, which equals negative 2. Alright. So this is gonna be 1 comma negative 2. So let's try 2 now just to stick with the positive numbers. This is gonna be 2 squared minus 3, which is just 4 minus 3, which equals 1. So this is the 2 comma 1 is our ordered pair over here. Alright? So now let's do the negative numbers. And so we've got y equals, and we've got negative 1 squared minus 3. Now negative one squared is just 1. So one minus 3 is negative 2, which is basically exactly what we got when we did this over here. This is just negative 2 over here. So this is negative 1 comma negative 2, and then last but not least, we have y equals negative 2 squared minus 3. This is actually just 4 minus 3, and we know exactly what that is. That just equals 1. So Our y value is 1, and so we have the coordinate negative 2 comma positive 1. Notice that there's, like, a weird symmetry that happens here. We got 1 negative 2, negative 3, negative 2, negative and then positive 1. So there's a weird symmetry that's going on here. So now that we're done with the second step, now we're just gonna move on to the 3rd step, which is gonna plot all these points over here. Right? So we did a lot a lot of calculations, but now we can just go ahead and plot and see what this graph looks like. So let's get started here. So this is the point negative 2 comma positive 1. So I'm gonna go over to my graph here, and this is gonna be negative 2 comma positive 1. Remember, you walk to the left, and then you go up to that value. Alright. So first x axis and then y axis. Now now we've got negative 1 comma negative 2. So we're gonna go to negative 1 and then down to negative 2. That's gonna be over here. Then we got 0 comma negative 3. So that's gonna be over here. And then we've got 1 comma negative 2. So this is now going to the right one and down 2, so that's over here. And then finally, we've got 2 comma 1. So we're gonna go over 2 and then up 1 over here. So notice how we've got so, again, sort of like the symmetry that we got here in the numbers actually ends up being sort of like a symmetry in, the points that we get here. And the last step we do is we actually just connect this with a curve or a line. If you try to connect this with a line, obviously, you can't do a line, that connects all these different points, so you're gonna have to connect it with a smooth curve. And, basically, what happens here is it's actually gonna look something like this. So you're gonna connect all these things here, and it's gonna look kind of like a u shape, and this is what that graph looks like. So this is actually called a parabola. We'll talk about these later on, but that's the graph for this equation. Thanks for watching.

2. Graphs

Two-Variable Equations

Precalculus

2. Graphs

Two-Variable Equations

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Multiple Choice

Graph the equation $y-x^2+3=0$ by choosing points that satisfy the equation.

Graph with a curve

Verified step by step guidance

Start by rewriting the given equation y - x^2 + 3 = 0 in a more familiar form. Add x^2 to both sides to get y = x^2 - 3.

Recognize that this equation is a quadratic equation in the form y = ax^2 + bx + c, where a = 1, b = 0, and c = -3. This represents a parabola that opens upwards.

Identify the vertex of the parabola. Since the equation is in the form y = x^2 - 3, the vertex is at the point (0, -3).

Choose a few x-values to find corresponding y-values. For example, if x = 1, then y = 1^2 - 3 = -2. If x = -1, then y = (-1)^2 - 3 = -2. Continue this for a few more points.

Plot the points (0, -3), (1, -2), (-1, -2), (2, 1), and (-2, 1) on the graph. Connect these points with a smooth curve to form the parabola, ensuring it opens upwards.