MB31 âReview Sheet 3 Answers
MB31 âReview Sheet 3 Answers MB31 âReview Sheet 3 Answers
5. Sketch the graph: a) 2 2 ( x 5) ( y 1) 4 + + − = b) 2 2 ( x+ 2) y + = 1 c) xy = 10 9 36 Circle with center at (-5, 1) Ellipse with center at (-2, 0) Equilateral hyperbola includes points: includes points: in Quadrants I and III (-7, 1), (-3, 1), (-5, 3), (-5, -1) (-5, 0), (1, 0), (-2, 6), (-2, -6) c) 2 2 x y − = 1 d) 36 16 y = − 2 2x 6 Hyperbola Parabola with x-intercepts at x =± 6 opens upward with y − int =− 6 6. An ellipse has its center at (-1, 2). Its minor axis is vertical and has a length of 8. Its major axis is horizontal and has a length of 10. Write an equation for this ellipse. 2 2 ( x−h) ( y−k) + = 1 2 2 a b 2 2 ( x+ 1) ( y−2) + = 1 25 16 Since the length of the axes are given, you need to divide them by two first and then square them to find the denominators. 7. Because Kelly’s coach believes that every player should get an equal opportunity to play, she varies the playing time so that it is inversely proportional to the number of players who show up for a game. When the whole team of 16 players attends, each player has 18 minutes of play time. How many players must be absent for Kelly to play for 24 minutes a) 12 b) 8 c) 6 d) 4 (18)(16) = 24x 288 = 24x x = 12 Since 12 players must be present, 4 players must be absent. 8. When David drives to Melissa’s college to visit her, his travel time varies inversely as his speed. If he drives at 56 miles/hour, he arrives in 3 hours. How many minutes would he save if he traveled at 60 miles/hour a) 80 b) 40 c) 28 d) 12 (56)(3) = 60x 168 = 60x x = 2.8 hours He would save 0.2 hours, which is 12 minutes.
9. If p varies inversely as q, find the missing value in the table: p 40 30 20 q 9 x 18 a) 4.5 b) 12 c) 15 d) 16 (40)(9) = 30x 360 = 30x x = 12 10. If a varies directly as b, and a = 28 when b = 8, what is a when b = 14 a) 49 b) 16 c) 3.5 d) 98 28 a = 8 14 8a = 392 a = 49 11. Each of the graphs is a transformation of the graph of y 2 = x . Find an equation for each of the functions. y =− ( x+ 4) 2 y = + + 2 ( x 1) 2 y = − − + 2 ( x 3) 2 12. Write an equation of the graph y 2 = x after the following transformation: a) Shifted 2 units to the left and 4 units up. b) Reflected in the x-axis, shifted 5 units down and 1 unit to the right. y = + + 2 ( x 2) 4 y =− − − 2 ( x 1) 5
5. Sketch the graph:<br />
a)<br />
2 2<br />
( x 5) ( y 1) 4<br />
+ + − = b)<br />
2 2<br />
( x+<br />
2) y<br />
+ = 1<br />
c) xy = 10<br />
9 36<br />
Circle with center at (-5, 1) Ellipse with center at (-2, 0) Equilateral hyperbola<br />
includes points: includes points: in Quadrants I and III<br />
(-7, 1), (-3, 1), (-5, 3), (-5, -1) (-5, 0), (1, 0), (-2, 6), (-2, -6)<br />
c)<br />
2 2<br />
x y<br />
− = 1<br />
d)<br />
36 16<br />
y = −<br />
2<br />
2x<br />
6<br />
Hyperbola<br />
Parabola<br />
with x-intercepts at x =± 6<br />
opens upward with y − int =− 6<br />
6. An ellipse has its center at (-1, 2). Its minor axis is vertical and has a length of 8. Its major axis is horizontal<br />
and has a length of 10. Write an equation for this ellipse.<br />
2 2<br />
( x−h) ( y−k)<br />
+ = 1<br />
2 2<br />
a b<br />
2 2<br />
( x+ 1) ( y−2)<br />
+ = 1<br />
25 16<br />
Since the length of the axes are given, you need to<br />
divide them by two first and then square them to find<br />
the denominators.<br />
7. Because Kelly’s coach believes that every<br />
player should get an equal opportunity to play, she<br />
varies the playing time so that it is inversely<br />
proportional to the number of players who show up<br />
for a game. When the whole team of 16 players<br />
attends, each player has 18 minutes of play time.<br />
How many players must be absent for Kelly to play<br />
for 24 minutes<br />
a) 12 b) 8 c) 6 d) 4<br />
(18)(16) = 24x<br />
288 = 24x<br />
x = 12<br />
Since 12 players must be<br />
present, 4 players must<br />
be absent.<br />
8. When David drives to Melissa’s college to visit<br />
her, his travel time varies inversely as his speed.<br />
If he drives at 56 miles/hour, he arrives in 3 hours.<br />
How many minutes would he save if he traveled at<br />
60 miles/hour<br />
a) 80 b) 40 c) 28 d) 12<br />
(56)(3) = 60x<br />
168 = 60x<br />
x = 2.8 hours<br />
He would save 0.2 hours,<br />
which is 12 minutes.
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