Download Intermediate Algebra Midterm II Solutions Name: ___KEY______

Intermediate Algebra Midterm II Solutions
Name: ___KEY______
Answers
1. Find the vertex of the parabola
.
1.
Solution 1:
Solution 2:
2. Solve for
==> Vertex =
:
[Hint: quadratic formula]
3. Find a quadratic equation with solutions 10 and –4, in standard form.
==>
3.
==>
4. Solve:
prod
2.
(use interval notation)
4.
---------0--+------+-----------------0---+-----0--+-----+------+-----0--+--0-----0---+---6
-2
1
5. Complete all the squares:
+
( x –
9
81 = 3 +
)2 =
6. Finish solving for x.
84
<--- 5. Fill in the squares
81
==>
==>
6.
7. Find the equation of the parabola thru points (–1, 2), (0, 3), (1, 6).
7.
==>
==>
==>
==>
==>
==>
,
8. Solve:
Let
. Then
8.
==>
==>
or
==>
Impossible!
9.
?
(round off your answer to nearest thousandth)
For problems 10 and 11 suppose that
&
9.
.
10.
11.
6.644
10. ______5, 25______
f −1 ( x) = ?
11.
==>
12. Suppose that
==>
, and
==>
Then
=?
12.
NOTE: Problem 12 wasn't the problem I meant to ask. Here's what I meant to ask:
Suppose that
, and
Then
=?
13. Solve:
13.
==>
14. Solve:
14.
==>
15. Solve:
==>
(round-off your answer to 4 decimal places)
==>
==>
15.
==>
16. Assuming unconstrained population growth... if there are 100 bacteria
at noon, and 500 at 1:00pm, how many will there be at 3:00pm?
16. _____12500______
==>
==>
==>
==>
17.
17. ______32_______
18. The longer leg of a right triangle is 7 cm longer than the shorter leg,
and the hypotenuse is 17 cm. Find the length of the shorter leg.
18. ______8_cm_____
==>
==>
==>
==>
==>
or
(but it must be positive)
On the same graph... graph:
19. the ellipse
20. the hyperbola
21. the hyperbola
( Label each graph with its problem number. )
22. Find the center of the ellipse
22.
23. Find the equation of the depicted ellipse, in standard form:
23.
Hint: center = (2, 1)
24. Find the equation of the circle with radius
and center
.
24.
25. Solve the system of nonlinear equations:
____________
==>
==>
==>
==>
25.
and