Question: Sketch 
. Give coordinates of each of the 4 vertices of the graph.
| Foundations
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| 1) What type of function is this? What type of graph is this?
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| 2) What can you say about the orientation of the graph?
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| Answer:
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1) Since both x and y are squared it must be a hyperbola or an ellipse. Since the coefficients of the Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x^{2}}
and  terms are both positive the graph must be an ellipse.
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| 2) Since the coefficient of the Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x^{2}}
term is smaller, when we divide both sides by 36 the X-axis will be the major axis.
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Solution:
| Step 1:
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| We start by dividing both sides by 36. This yields Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{4x^2}{36} + \frac{9(y + 1)^2}{36} = \frac{x^2}{9} + \frac{(y+1)^2}{4} = 1}
.
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| Step 2:
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| Now that we have the equation that looks like an ellipse, we can read off the center of the ellipse, (0, -1).
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| From the center mark the two points that are 3 units left, and three units right of the center.
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| Then mark the two points that are 2 units up, and two units down from the center.
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| Step 3:
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| Now draw an oval through the four points you just drew.
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