Find an equation for the graph sketched below-4 ~3 -2 -1X 2 3 4 52 335-8f(c)Preview...

Sketch the graph of each equation. $\frac{(y+4)^{2}}{4}-\frac{x^{2}}{25}=1$

So far this problem because our equation is given to us in standard form. I've decided that I want to just create my graph by finding my ex and why intercepts and then connecting those two points with the straight line. I'm so to calculate our X intercept we're going to substitute y is equal to zero into our equation. So when we do that, we get a four over five is equal to negative 1/3 ex minus 3/4 time zero So we can see that this term is going to go away and to solve for X, we're going to have to multiply everything by negative three. So our X intercept is going to be negative 12 over five zero so we can go ahead and plot this on our graph right away. So we know that negative 12 5th is going to be a little bit to the left of negative too, which will be right about here and next. We can calculate, or why intercept by plugging in X is equal to zero into our equation. So when we do that, we get 4/5 is equal to negative 1/3 time, zero minus 3/4. Why? And so to Seoul for why we're going to multiply everything by negative four over three. So when we do this, um, our equation is going to be negative. 16 over 15 is equal to you. Why? So we can see that our why intercept is going to be just a little bit below negative one, which will lie right about here. I'm in. So now that we have our points, we can go ahead and connect them with the straight line in order to get the graph of our equation.

In this problem, we want to scratch the graph of X plus three squared plus y minus four squared equals 25. This question is challenging understanding of comic sections and graphical transformations of chronic sections to solve when you have an understanding of the difference between comic sections and limiting forms. Common comment sections are those on the left, parabolas, hyperbole, ellipsis, limiting forms, or those on the right lines, empty sets, circles and points. If we identify which of the forms are equation X plus three squared, but it's like it's forced critical 25 tanks. We can easily graph and transform the graft to solve. So our simplified equation is already given. We see that we have the form of a circle X squared plus Y is critical R squared. We have a shift left and three Shift upwards of four And a radius and five for the circle. Thus for raising circle five under the origin in black, we shift left three up four to obtain this new circle in red, as is shown in the graph on the right.

To graph our equation. X plus five squared over four plus y minus two. Squared over 36 is equal to one we confined. His identifying information or center are a value in R B value list center. Is there a dinner is going to be defined at the point H and K, We can compare our equation with the standard equation to see what they are. From here. We can see that our H value is gonna have to equal negative five cancel out negative ways in in our K value is going to be equal to do. This means that our center is to find a point negative five to okay for a value we can compare this a squared with four a squared is equal to four. That means that are a value is equal to the square root of four as we can take the spirit of both sides. So if a is equal to the square to four, which is just two, that means ese go to with the same thing. For R B. Value B squared is equal to 36 so B is equal to the square to 36 or just six Okay, now we have enough information to graph Center is at negative five. So we'll do a dot right there for the center, okay? And are a value. This is gonna be our horizontal size of our lips. If it's it's too. I'm gonna make Vergis ease to left and to the right of our center and r B values. Eagle six. This is gonna be the vertical size of our lips. So going to do, we're to see six above and six below our center. Okay, now that we have our vergis is we can't sketch our lips. All right, This is the rough sketch for your lips. For our equation. X plus five squared over four plus y minus two. Squared over 36 is equal to one. Our center is at negative 52 are a value is equal to two and R B value is equal to six