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Draw a quick sketch of the graph of each equation.$$x=y^{2}$$...

Question

Draw a quick sketch of the graph of each equation.$$x=y^{2}$$

Draw a quick sketch of the graph of each equation. $$ x=y^{2} $$



Answers

Draw a quick sketch of the graph of each equation. $$ x=y^{2} $$

They have to plot the graph of the equation that by is equal to Underwood effects. So let's take a few values, affects and by So when X is zero, then by zero when X is one, then vise one when excess four then by is to when x is nine. Then why is three when X is 16? Then vie is four. Now let's plot the graph using the decimal software. So the graph off the given function will look something like this been blotted on the coordinate access.

We have to plot the graph off decoration. Why is equal to one divided by its So let's take a few values off X. Invited to plot the graph when it's is minus two, then by is minus 0.5 when X is minus one, then by is also minus one when X is one, then by is one been excess to then by is 0.5 when X is four, then why is 0.25 not taking these values at the function? Let's photograph on the decimal software. So the graph of the given function will look something like this, and clearly the function is not defined at the origin or zero.

Half an equation of an ellipse. We know that the standard form foreign lips equation has x squared over a squared plus y squared over B squared equals one. The equation that were graphing for this problem has x squared. Plus why squared divided by four equals one. So it's similar to our standard form of our lips equation. We know that the four underneath the Y squared is our B squared value. So we can say that be is equal to plus or minus two. These are gonna be our why intercepts of our graph this X squared doesn't have a fraction. There's nothing directly underneath the X squared value to give us our A squared. But we can always think of anything that doesn't have a denominator as the one in the denominator. And so if we put X squared divided by one, what we have is our A squared value is one which gives us plus or minus one as a so those are our ex intercepts. What's on top of this equation is an X squared and a Y squared, which means that the center of this ellipse is at the origin 00 So we scroll over to my does Mose calculator grid scream. We can sketch the graph. We'll put our two and minus two as our Y intercepts the one and negative one. As our ex intercepts this ellipse again centered at 00 so I can sketch. This is the left half of my lips and the right half of my lips. And here we have the equation. X squared plus y squared over four equals one steps as any lips.

Catch the graph of an equation and this equation is gonna be any lips. The standard form for any lips is this equation X squared, divided by a squared plus y squared divided by B squared equals one. Our problem is asking us to sketch X squared plus y squared over four equals one. We can see that the Y squared piece is in the standard form where there's a fraction. Why scared on top? A number on the bottom, the X squared pieces not necessarily in the standard form. Although if we wanted to, we could put divided by one here to make a fraction out of it. We now have the standard form for our lips equation, and we can see that the one under the X squared is my A squared value. So that makes a plus or minus one. And because they are under the X squared value, these a plus or minus one pieces air gonna be my ex intercepts. The four is my B squared value, which would make B plus or minus two because they're under the Y squared value. These are my why intercepts the X squared in the Y squared alone on the top of the fractions puts this he lips with a sinner at the origin 00 so I can put my plus or minus one on my ex intercepts and my plus or minus two or my why intercepts and sketch my lips out. This would be the left half, and the right half centered out the origin we have my equation X squared plus y squared over four equals one, which is the equation of the sea lips.


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