Matt Lee at 06:56, 14 April 2015

2015-04-14T06:56:09Z

Matt Lee at 22:25, 6 April 2015

2015-04-06T22:25:15Z

Matt Lee: Created page with "'''Question: ''' Sketch $4x^2 + 9(y + 1)^2 = 36$ . Give coordinates of each of the 4 vertices of the graph. {| class="mw-collapsible mw-collapsed" style = "text-ali..."

2015-03-23T02:50:21Z

Created page with "'''Question: ''' Sketch <math>4x^2 + 9(y + 1)^2 = 36</math>. Give coordinates of each of the 4 vertices of the graph. {| class="mw-collapsible mw-collapsed" style = "text-ali..."

New page

'''Question: ''' Sketch <math>4x^2 + 9(y + 1)^2 = 36</math>. Give coordinates of each of the 4 vertices of the graph.

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!Foundations
|-
|1) What type of function is this? What type of graph is this?
|-
|2) What can you say about the orientation of the graph?
|-
|Answer:
|-
|1) Since both x and y are squared it must be a hyperbola or an ellipse. Since the coefficients of the <math>x^2</math> and <math>y^2</math> terms are both positive the graph must be an ellipse.
|-
|2) Since the coefficient of the <math>x^2</math> term is smaller, when we divide both sides by 36 the X-axis will be the major axis.
|}

Solution:

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
|We start by dividing both sides by 36. This yields <math>\frac{4x^2}{36} + \frac{9(y + 1)^2}{36} = \frac{x^2}{9} + \frac{(y+1)^2}{4} = 1</math>.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
|Now that we have the equation that looks like an ellipse, we can read off the center of the ellipse, (0, -1).
|-
|From the center mark the two points that are 3 units left, and three units right of the center.
|-
|Then mark the two points that are 2 units up, and two units down from the center.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 3:
|-
|Now draw an oval through the four points you just drew.
|}

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		+	[[8AF11Final\|<u>'''Return to Sample Exam</u>''']]

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 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 ! Step 3:
 |-
 |Now draw an oval through the four points you just drew.

8A F11 Q6 - Revision history

Matt Lee at 06:56, 14 April 2015

Matt Lee at 22:25, 6 April 2015

Matt Lee: Created page with "'''Question: ''' Sketch 4x^2 + 9(y + 1)^2 = 36. Give coordinates of each of the 4 vertices of the graph. {| class="mw-collapsible mw-collapsed" style = "text-ali..."

Matt Lee: Created page with "'''Question: ''' Sketch $4x^2 + 9(y + 1)^2 = 36$ . Give coordinates of each of the 4 vertices of the graph. {| class="mw-collapsible mw-collapsed" style = "text-ali..."